What is the government's obligation to prove that the inevitable discovery exception to the exclusionary rule applies?

To show that the inevitable discovery exception to the exclusionary rule applies, the burden is on the Government to prove that each event leading to the discovery of the evidence would have occurred with a sufficiently high degree of confidence for the district judge to conclude, by a preponderance of the evidence, that the evidence would inevitably have been discovered. United States v. Vilar , 729 F.3d 62, 84 (2d Cir. 2013). We have previously characterized the Government's obligation as one of certitude that the evidence would have been discovered. Heath , 455 F.3d at 58 n. 6.