The Problem Of Induction And Free Will

Determinism is the belief that any event, the way it turns out, is fixed and can't be otherwise by relevant events that precede said event.

Determinism is, in my humble opinion, completely reliant on observations of the natural world where, indeed, as claimed, there's a causal connection between events such that past events shape the future in ways that "preclude" any deviation from established patterns of matter-energy interaction.

The concept of causality supervenes on the principle of the uniformity of nature. If there's no uniformity it implies there are no patterns and if there are no patterns, causality which is a pattern becomes meaningless.

However, the principle of the uniformity of nature suffers from a serious flaw viz. it can't be proven deductively which is, in different words, the problem of induction. Simply put, there's an unignorable uncertainty in re the principle of the uniformity of nature. By that token, causality too is rendered uncertain. Doesn't it follow then that determinism, at the very least, is somewhat less credible than it's made out to be?

Free will finds a cozy niche in the inherent uncertainty of causality which itself is implied by the problem of induction. No?