The human-level argument for complexity reducing probability something like A∩B is more probable than A∩B∩C because the second has three fault-lines, so to speak, and the first only has two, so the second is more likely to crack.

Strictly speaking, the Pr(A∩B) ≥ Pr(A∩B∩C), not Pr(A∩B) > Pr(A∩B∩C). Otherwise, excellent post.