Find the conditional expectation $E[X \mid X \leq p]$

Let $X$ be a discrete random variable that can take values from 1 to $n$, where $n$ is a large fixed number and also let $p\ll n$ be a fixed number. I am trying to find the expectation $$E[X \mid X \leq p].$$

I know how to compute $E[X \mid X = p]$, but I have no idea how to proceed to compute that expectation.