I was reading the answer of Hypnosifl on What's wrong with this experiment showing that either FTL communication is possible or complementarity doesn't hold?
If we assume that:
Alice is at D1/2/3/4 and replaces BSA and BSB with mirrors (so we always lose the 'which-path-information')
Bob is at D0 and makes his measurement first
Now let's say Bob sees his photon landing right in the middle of his screen, why doesn't this alter the probabilities of the entangled photon ending up in D1/2? It seems from the interference patterns that in the case of photons landing in the middle of the screen there is a much stronger correlation with D1 than D2 (maybe 90%/10%).
So basically the question is why is P(D1) = P(D1|D0)? Or isn't it?