When my teacher told us about the chain rule I found it quite easy, but when I am trying to prove something based on this rule I kind of get confused about what are the allowed forms of this rule. For example, I can't understand why I can say:
$$ p(x,y\mid z)=p(y\mid z)p(x\mid y,z) $$
I can not understand how one can end up to this equation from the general rule! Can you please help how to think correctly about this rule?
I found this post useful for my question: