I have two sets $M$ and $H$. $M$ is an arbitrary string of length $k$ and $H$ is an string of length $p$. Both are constructed from a charset of length $r$. And $p<k$.
Hash function $f(m)=h$.
I understand that $r^p$ hashes are possible and that $r^k-r^p$ collisions occur for the complete set $M$.
But how can I predict the overall probability for finding any element of $M$ that correctly maps to a given element of $h$?