How do you interpret this formula of a density function?

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I have the following formula: https://i.stack.imgur.com/qxnWv.png Y and Z are variables with density functions. f_(Y=y)(z) what is that? the density of y given z? As far as i understand the right side is the joint density of y,z divided by density of y, i am mostly unsure about the left side. Tyvm in advance

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It’s the conditional probability that $Z=z$ given $Y=y$. Hope this helps!