I'm in a ML course, and we had this math refresher quiz. We were asked to prove (or disprove) the following: $$p(a | b,c) = p(a|c) \to p(a|b) = p(a).$$
It is clear that $a$ is not dependent on $b$, when both $b$ and $c$ occur. However, it is not fully clear wether this implies that $a$ itself is independent of $b$. Intuitively, yes. But I don't know how to prove that mathematically. Any suggestions?