Which conditions are assumed in $P(z|x_1,y_1,...,x_n,y_n)=\Pi_{i=1}^n P(z|x_i,y_i)$

Question

Which conditions are assumed under this equation:

$P(z|x_1,y_1,...,x_n,y_n)=\Pi_{i=1}^n P(z|x_i,y_i)$

It is written that we are assuming the independence. But I'm curious that which random variables are assumed to be independent.