statistics – Conditional distribution of two random variables.

Suppose I have two continuous random variables $$X$$ and $$Z$$. Although I know that $$Z sim mathcal {N} (0, 1)$$, I have no information for the distribution of $$X$$. Now, one of my friends said that conditional distribution $$p (Z | X)$$ should also be a Gaussian.
I do not know if it's ok or not?