This appeal of a criminal conviction presents extraordinary facts that challenge a reviewing court to take seriously its constitutional obligation to assure that evidence resulting in a conviction was sufficient to permit a jury reasonably to find guilt beyond a reasonable doubt. Jeremiah K. Clark appeals from the March 7, 2012, judgment of the District Court for the Northern District of New York (William M. Skretny, District Judge), convicting him, after a jury trial, of being a felon in possession of a firearm (Count I) and possession of a controlled substance (Count II). We have affirmed the conviction on Count I in a Summary Order filed today. In this opinion, we reverse the conviction on Count II.
Background
On Nov. 16, 2002, officers from the City of Lockport Police Department (Lockport, N.Y.) and the Niagara County Sheriffs Office (Lockport, N.Y.), responded to a 911 call reporting that a group of men, possibly armed, had just left Gonzo’s Bar in Lockport in a white Jeep Cherokee after trying to “jump somebody.” When the officers arrived at the bar, they saw Clark and three others sitting in the Cherokee. The facts of the ensuing confrontation, detailed in a Summary Order filed today, are not relevant to the issue decided in this opinion, except to note that the police found a firearm in the Cherokee and arrested Clark. In this opinion, we are concerned only with the facts occurring after Clark’s arrest.
Niagara County Deputy Sheriff Anthony Giamberdino placed Clark, alone, in the rear compartment of his police cruiser. Clark was handcuffed with his hands behind his back. Niagara County Deputy Sheriff Gary May testified that the link between the two bracelets of the handcuffs was no longer than one or one and one-half inches. City of Lockport Police Officer Steven Abbott testified that before Clark was placed in the car, he patted down his waist, pockets, pant legs, and coat, looking for weapons. Nothing was found. The ride from the scene of the arrest to the Lockport police station lasted about one minute. After arriving at the police station, May helped Clark, still handcuffed, out of the ear. Clark was then escorted into the booking area of the police station.
Once Clark was out of the police car, Giamberdino lifted the cushion of the back seat out and up, making visible the space between the back of the back-seat cushion and the bottom of the back-seat back rest. In that space he saw a quantity of a white powdery substance that later analysis determined was crack cocaine. Giamberdino also testified that he had checked this space before starting his evening shift, nothing was there at that time, and Clark was the first person to occupy the back seat of the car that evening.
Deputy Sheriff May testified that as Clark got out of the car and walked past him, he did not see any white powdery substance on his hands, pants, or jacket. Nor did he see any white powdery substance on the back seat until the seat was lifted up. No glassine envelope or other container was found in the police car or on Clark’s person.1
*811Discussion
We fully understand the standards for appellate review of a jury’s finding of guilt. We are to view the evidence “in the light most favorable to the prosecution,” Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979), and determine “whether the record evidence could reasonably support a finding of guilt beyond a reasonable doubt,” id. at 318, 99 S.Ct. 2781 (footnote omitted). A defendant challenging the sufficiency of the evidence “bears a heavy burden.” United States v. Hassan, 578 F.3d 108,126 (2d Cir.2008). All reasonable inferences are to be drawn in the prosecution’s favor, and we are to defer to the jury’s assessment of the witness’s credibility. See United States v. Sabhnani, 599 F.3d 215, 241 (2d Cir.2010). The deference to the jury’s verdict required by these standards does not mean, however, that we must never deem evidence insufficient. Nor does it mean that if there is any evidence arguably in support of a verdict, we must affirm.2 Of course, the issue is not whether ive believe the evidence does not prove guilt beyond a reasonable doubt. See Jackson, 443 U.S. at 318-19, 99 S.Ct. 2781. But if we are to be faithful to the constitutional requirement that no person may be convicted unless the Government has proven guilt beyond a reasonable doubt, we must take seriously our obligation to assess the record to determine, as Jackson instructs, whether a jury could reasonably find guilt beyond a reasonable doubt.
In our view, this record does not permit an affirmance on Count 2. Several facts are not in dispute: (1) Clark was patted down for weapons before being placed in a police car; (2) no object large enough to contain a substantial quantity of crack cocaine was noticed; (3) Clark was then placed in the back of a police car with his hands handcuffed securely behind his back; (4) the ride to the police station took about one minute; (5) shortly after Clark got out of the vehicle, with his hands still handcuffed behind his back, a police officer lifted the back seat cushion sufficiently to disclose the space between the back edge of the back-seat cushion and the lower edge of the back-seat back rest; (6) in that space the officer found a quantity of crack cocaine measuring more than five inches in length and about one inch wide, and of sufficient depth such that some quantities of crumbled crack cocaine are visible above the layer of fully powdered crack cocaine (a photograph of the crack cocaine appears in the Appendix to this opinion); (7) no traces of crack cocaine were observed on Clark’s clothing or on his hands; (8) no glassine envelope or similar container customarily used for holding a quantity of crack cocaine was found in the police car, nor was Clark observed to have discarded such a container after leaving the police car.3
*812There are only three possible ways that this quantity of crack cocaine could have been secreted in the space in which it was discovered. (1) Clark might have removed the quantity from his person or clothing and wedged it into the space underneath the seam where the back-seat cushion meets the back-seat back rest; (2) someone other than Clark might have inadvertently left the crack cocaine in that space before Clark entered the police car; (3) someone other than Clark might have deliberately placed the crack cocaine in that space after Clark got out of the police car. Clark’s conviction for possessing crack cocaine is valid only if a jury could reasonably find the first possibility beyond a reasonable doubt.
We cannot say it is an absolute impossibility for a person with his hands securely handcuffed behind his back to extract a substantial quantity of crack cocaine from his person or clothing and wedge it into the space where the quantity was found without leaving a trace of cocaine on his fingers or clothing, but we can say that the possibility of such an occurrence is so exceedingly remote that no jury could reasonably find beyond a reasonable doubt that it happened. The remote possibility is diminished virtually to zero by the fact that no glassine envelope or other packaging material was found in the police vehicle or on Clark’s person. It taxes credulity to think that Clark carried such a quantity of crack cocaine loose in his pocket and, while handcuffed, extracted it from his pocket and secreted it where it was found, all without leaving a trace on his person or clothing.
Whether or not the extraordinary improbability of circumstances necessary for conviction on Count II in fact occurred, it is better to honor the constitutional standard of proof beyond a reasonable doubt by appropriate appellate review than to require Clark to serve three extra years, in addition to the ten years for Count I, for an offense of which he is highly likely to be innocent.
It has been said that it is better to let ten guilty persons go free than to convict one innocent person.4 In the past, some have favored higher ratios.5 However one *813prefers to quantify an unacceptable risk of convicting the innocent, it is difficult to imagine a case where the possibility that an innocent person has been convicted of an offense is greater than the one now before us.
Conclusion
The judgment is affirmed with respect to Count I and reversed with respect to Count II.
Appendix
[[Image here]]
This photograph was taken looking down into the space between the bottom of the back of the back seat and the back of the back-seat cushion. The object across the middle of the photograph is a ruler.
. Giamberdino testified that he saw a lighter on the back seat. Although the Government's brief says that Giamberdino "observed a white powdery substance on the back seat,” Brief for United States at 3 (emphasis added), the cited pages, Tr. 446-47, contain no such statement. On cross-examination, Giamber-dino testified, "Deputy May saw a lighter on *811the seat, and I went to grab it, and then I just did my check right there, and that’s when I noticed the white powdery substance.” Moreover, there is no testimony that any officer saw traces of cocaine on the lighter or looked at the insides of Clark’s pockets to see if there were traces of cocaine there, a logical thing to do if they thought Clark had brought the cocaine into the car.
. A conviction in the absence of any evidence to support a jury’s guilty verdict violates the Due Process Clause, see Thompson v. City of Louisville, 362 U.S. 199, 206, 80 S.Ct. 624, 4 L.Ed.2d 654 (1960), whereas the existence of evidence of insufficient probative force to permit a jury reasonably to find guilt beyond a reasonable doubt violates the reasonable doubt standard constitutionalized by In re Winship, 397 U.S. 358, 363-64, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970).
. One additional'item of evidence is arguably relevant. Lt. Michael Costello testified that at the police station Clark said, "I’ll confess to everything if you let my cousins go.” Howev*812er, there is no testimony that Clark saw the cocaine after Giamberdino lifted up the seat cushion or otherwise became aware that it had been discovered. After he got out of the police car, Clark was escorted to the booking area of the Lockport police station. Both May and Costello testified that Clark was in the booking area of the Lockport police station when Giamberdino discovered the cocaine. Thus, there is no basis to believe that Clark's offer to confess (accepting that he did say it) applied to any offense conduct other than the disturbance at the bar that had given rise to the 911 call and his possession of a weapon. Even if the jury inferred that Clark's offer to confess to "everything” covered the cocaine, that inference would not be reasonable since it would have been undermined by the virtual impossibility of Clark’s having secreted the cocaine behind the seat cushion while handcuffed and without leaving a trace on his clothing or person.
. See Furman v. Georgia, 408 U.S. 238, 367 n. 158, 92 S.Ct. 2726, 33 L.Ed.2d 346 (1972) (Marshall, J., concurring) (quoting William O. Douglas, "Foreword” to Jerome Frank & Barbara Frank, Not Guilty 11-12 (1957)); Goetz v. Crosson, 967 F.2d 29, 39 (2d Cir.1992) (Newman, J., concurring); Bunnell v. Sullivan, 947 F.2d 341, 352 (9th Cir.1991) (in banc) (Kozinski, J., concurring); United States v. Greer, 538 F.2d 437, 441 (D.C.Cir.1976); see also 4 William Blackstone, Commentaries *358.
. See Sir John Fortescue, De Laudibus Legum Angliae 65 (S.B. Chrimes ed., Cambridge Univ. Press 1942) (1471) (20 to 1); Thomas Starkie, Evidence 756 (1724), quoted in DC Wigmore on Evidence § 2497, at 409-10 (Chadbourn rev.1991) (99 to 1).