exactly, (X => Y) <=> (!Y => !X) should be more known

Eh? (P(X|Y)>P(X) iff P(Y|X)>P(Y)) whenever all the relevant probabilities (P(X), P(Y), P(X and Y), etc.) are strictly positive and strictly less than 1.

Now, X might be much stronger evidence for Y than Y is for X, but if Y is evidence for X, then (assuming the previously mentioned assumption) then X is evidence for Y, even if only very weak.

Yes but the comment being responded to stated “but there are Y that are not X” which was categorical.

Sorry, I don’t understand this point. What’s the interpretation of your previous message (in light of that) which makes it true?