I am late to this discussion and am unlikely to catch up at this point. What I really wanted to note is the importance of agreeing to a sample space first, and then we can make statements about independence. We should generally avoid making statements like P(H) != P(H|E) and then seeking out a sample space such that it is true (that’s cheating!).
Except, within an agreed frame where P(H) = P(H|E) should be true, we might find contradictory evidence. Strong evidence might be cause to adjust our frame. This is a mirror to the scientific method and Bayesian learning models. Without going back to read everything, I’m guessing this might be part of the discussion already. 