How to find the conditional probability for the following distribution?

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Suppose I have communication channel where $h$ is $CN(0,\sigma_h)$ and n is $CN(\mu,\sigma^2)$. Both h and n are complex Gaussian random variable. My channel model is as following.
$y=hx+n$
Here x is a complex input. I have two question.
1. What is $p(y|x)$?
2. if $h$ and $n$ are vector what will be $p(y|x)$