Conditional Independence

Suppose we have random variables $X$, $Y$, and $Z$ over domains $A$, $B$, and $C$. We say $X$ is conditionally independent of $Y$ given $Z$ if for all $a \in A$, $b \in B$ and $c \in C$ we have

$$\mathbb{P}[X = a \vert Y = b, \ Z = c] = \mathbb{P}[X = a \vert Z = c].$$