William Edward Morris and Charlotte R. Brown present a view of Hume's idea of causation that may help resolve the OP's question whether probability could justify causal inference through reason or understanding.
As the OP notes, effects are not necessarily true given past events believed to be causes of those effects. So, one cannot justify causal inference through relations of ideas, that is, there is no necessary connection between past events and future events.
To consider probability is to consider matters of fact rather than relations of ideas as a rational justification for causality. According to Morris and Brown, Hume also rejects matters of fact, that is, probability, as a rational justification for causal inference: (Section 5.1)
Hume argues that there is no probable reasoning that can provide a just inference from past to future. Any attempt to infer [a future prediction] from [a past experience] by a probable inference will be viciously circular—it will involve supposing what we are trying to prove.
Hume spells out the circularity this way. Any reasoning that takes us from [a past experience] to [a future prediction] must employ some connecting principle that connects the past with the future. Since one thing that keeps us from moving directly from past to future is the possibility that the course of nature might change, it seems plausible to think that the connecting principle we need will assure us that nature is uniform—that the course of nature won't change—something like the uniformity principle:
Establishing this uniformity principle is what prevents both relations of ideas (necessary truths) and matters of fact (probability) from providing a justification of causal inference using reason or understanding.
Hume offers "custom or habit" as alternatives to reason and understanding to explain why we make causal inferences: (Section 5.2):
Since we're determined—caused —to make causal inferences, then if they aren't “determin'd by reason”, there must be “some principle of equal weight and authority” that leads us to make them. Hume maintains that this principle is custom or habit:
They quote Hume:
whenever the repetition of any particular act or operation produces a propensity to renew the same act or operation … we always say, that this propensity is the effect of Custom. (EHU 5.1.5/43)
Here are the questions:
However, would Hume concede that certain events have a higher probability of occurring based on past events? Is it much more likely that a rock will break a window when thrown with a certain force than not? Or is that a fallacious argument grounded in confusing the "constant conjunction of events" (of always seeing rocks break windows) with causality?
Hume accepts "custom or habit". He does not accept probability through reason or understanding. That is, neither relations of ideas nor matters of fact (probability) provide a rational justification for causal inferences.
Morris, William Edward and Brown, Charlotte R., "David Hume", The Stanford Encyclopedia of Philosophy (Spring 2017 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/spr2017/entries/hume/.