## Poisson distribution: daily number X of cheques

The daily number $X$ of cheques presented at a local branch of a certain bank to be cashed has the following probability mass function (a Poisson distribution with parameter $\lambda$):

$p_X(k)=e^{-\lambda}\frac{\lambda^k}{k!}$ for $k=0,1,2,...$

If each cheque presented has a probability $p$ to be refused (due to the lack of sufficient funds), compute the pmf, $p_S(s)$ for $s=0,1,2,...$, of the daily number $S$ of refused cheques.
A hint was provided as follows: You may first compute the conditional probability $P(S=s|X=k)$ and then use the total probability formula by summing over all possible values of $k$.

I'm still grasping the concepts behind Poisson distributions, so any help would be appreciated.