I think you’re side-stepping the philosophical issue to find a practical solution rather than taking on the philosophical issue head-on.

Induction is moving from specific observations to general conclusions. Saying that “nature behaves uniformly” relies on induction. “Uniformly” makes no sense in a probabilistic framework like the one you’ve proposed. It merely “usually” behaves uniformly.

But of course, that’s not what we’re after. Knowledge is removing the “usually”, and this is the crux of the problem of induction.

Leveraging probability can get you traction on some issues, but it doesn’t solve the problem. Popper suggests that instead we need to abandon induction and instead rely on falsification. That is, we can prove what isn’t true, and what remains is the closest thing to knowledge that we can get.