I have a simple question about conditional probabilities and independence, suppose that $X, Y$ are independent random variables while as well $N$ is a random variable (which both $X$ and $Y$ are independent to). Would it follow that the conditional random variables $X|N$ and $Y|N$ are independent random variables as well? If this is the case, what would be a proof of this? I've had this question for a while.
Thanks for the help.