# Sample $k$ of $n$ numbers (with replacement), what is the probability for a certain from the $n$ numbers to be the median of the $k$ numbers [closed]

Suppose we have ordered numbers $$a_1 < a_2 < \dots < a_n$$. Now we sample $$k$$ of them with equal probability and with replacement and compute the median of these and call it $$m$$. (Let us assume that $$k$$ is odd for the sake of simplicity.) What is the probability the $$m = a_i$$ for each $$i$$?

I want to know this to construct the probability mass function for the median of $$k$$ random draws from a sample of $$n$$ numbers.