I suddenly remembered a quote from a math humor book I read back in junior high. It went something like this:
"The laws of probability are so cleverly formatted that no experiment can refute or prove their validity."
It won't surprise me if there's been a lot of debate about this that may have settled the issue centuries ago, but I haven't been able to come up with a way to falsify the laws of probability from my armchair bit of math. Any particular experimental result is possible under the laws of probability: Some are just more probable than others, and there's no magical cutoff for improbability.
If I can't get anywhere with them, I think I might just have to stick them into the same category of assumptions as "the external universe exists" and "the laws of physics are consistent."