Given two discrete RVs $X$ and $Y$ with joint pdf $f_{xy}(x,y),x\in\mathscr{X},y\in\mathscr{Y}$, the conditional pdf of $X$ given that $Y=y$ is denoted by $f_{X|Y}(x|y)$ and defined as $$f_{X|Y}(x|y)=\frac{f_{xy}(x,y)}{f_y(y)}, \ x\in\mathscr{X}, \ f(y)>0$$