Formula for conditional mutual information What will be the formula for I(X;Y|Z,W)? Given:
I ( X ; Y | Z ) = H ( X , Z ) + H ( Y , Z ) − H ( X , Y , Z ) − H ( Z ) 
                = H ( X | Z ) − H ( X | Y , Z ) 
                = H ( X | Z ) + H ( Y | Z ) − H ( X , Y | Z ) 


Thinking $Z$ as a vector random variable, you can simply write
$$ I(X;Y|Z,W) = H ( X | Z,W ) + H ( Y | Z,W ) − H ( X , Y | Z,W )$$
