Right Neil (and George). But the reason for that inability to distinguish empirically is that, whilst probability is an empirical science, it is only a comparison of propositions in particular circumstances (probably most closely allied to logic).
“Chance”, however (in the sense of ontological randomness I’ve been using here) is a metaphysical assumption used as a theoretical explanation of probability. “Choice” is an alternative metaphysical explanation of the same phenomena.
As is always the case, the metaphical choice you make depends on non-empirical matters - though it might, indirectly, include such things as empirical evidence for God.
A caveat to that is that if we talk about chance in the Thomistic sense of the accidental confluence of lawlike events (eg two planets in eccentric orbits eventually colliding, or happening to meet an old friend in an unexpected location, or the trajectories of particles in a gas), then the “chance” is real, but purely epistemological: in theory , but not always in practice,we can empirically distinguish it from choice, by plotting the orbits of the planets, by interviewing the friends for their reasons for being there, by getting hold of Maxwell’s demon to track molecules, etc.
Nevertheless, this does not exclude providential choices from these areas, because we never know everything accurately enough to account for the whole phenomenon.