"Proof" by evidence is an inherently statistical process. E.g. cops find a DNA match between a suspect and skin cells found under a murder victim's fingernails under circumstances where it is clear she tried to fight off her attacker. Does that "prove" guilt? No, it proves that under similar circumstances, guilty is highly likely. The problem is not that the justice system is statistical. That's unavoidable. The problem is the unfortunate confluence of the low standard of proof ("more likely than not" versus "beyond a reasonable doubt") combined with the high ratio of illegal versus legal reasons for carrying large amounts of cash (i.e. a high prior odds ratio).

FWIW (Rayiner knows this, but maybe everyone else doesn't):

The concept of "proof of innocence" does not appear in the Constitution; it derives from common law, and the Latin word it comes from doesn't mean "prove" in the mathematical sense.

Which makes sense, because "innocent until formally proven guilty" doesn't make sense in a sentence that proceeds to "beyond a reasonable doubt".

And it's interesting, too, how often people go in the other direction, and seem to think "any shred of theory, however improbable, means you can't be found guilty", and attempt to try to classify it as "beyond any/all doubt".

Yes, but statistically analyzing the likelihood of guilt using given evidence is different than arbitrarily linking blanket cases where there is no defined connection. Just saying "cash is suspicious so we are allowed to seize it whenever we see a lot of it" is a blatant violation of property rights. There is absolutely no crime that can be linked directly to cash ownership.