conditional probability on the sum of two random variables

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If I have $ X=Y+Z $ and $Y$ and $Z$ are independent, what is the high-level formula for finding $p(y|x)$? I was able to find the $p(X)$ using convolution but I am a little lost afterward wrt which formula should I use? Like in normal case (not a sum of two independent random variables) I know I should use $\frac{p(x,y)}{p(x)}$ however in this case, not sure what is the proper formula.