I think the legal system understands quite well that it doesn't prove anything (in the mathematical sense), which is why it has different standards of proof. A

I think the legal system understands quite well that it doesn't prove anything (in the mathematical sense), which is why it has different standards of proof. A 1 in 1 trillion chance would be considered both "beyond reasonable doubt" (enough for criminal matters) and satisfy the much weaker "balance of probabilities" usually applied to civil matters. Of course there are plenty of examples to point to where people were convicted despite very reasonable doubt.