For all discrete probabilities $P$ and all events $X$ and $Y$, prove or disprove:
If $0 < P(X) \leq P(Y)$, then $P(X|Y) \leq P(Y|X)$.
My attempt goes something like this (which I am sure is wrong):
Consider $X$ and $Y$ are independent of each other.
Since $P(Y) \geq P(X)$, $p(Y|X) = 0$ and $P(X|Y) \leq 0$.