# conditional pdf and joint pdf

I am looking at a description of a process that says

$$f(y|a_1,z,a_0) = \dfrac{f(y,a_1,z,a_0)}{p(a_1|z,a_0)p(z|a_0)p(a_0)}$$

I am not sure if I follow this joint pdf, conditical pdf , p(.) relation. Need help understanding this with an example. Sorry for a seemingly vague question. I will delete this question if this unclear.

This looks to be a version of the probability chain rule. Since $$f(y, a_0, z, a_1) = f(y | a_0, z, a_1) \times p(a_1 | z, a_0) \times p(z | a_0) \times p(a_0)$$. You can divide through by the last three terms in my equation to arrive at your equation.