Substring Probability

You are given two strings $P$ and $Q$. Consider some uniformly randomly and independently chosen non-empty prefix $X$ and non-empty suffix $Y$ of $P$. A string $Z$ is formed by concatenating $X$ and $Y$ in this order. Find the probability that $Z$ is a substring of $Q$. It can be shown that the answer can be represented as a fraction $U/V$, where $U$ and $V$ are non-negative integers and $V$ is