If $X,Y,Z$ are three different random variables, and let H($\cdot$) determine entropy, is it true that
$H(X|Y,Z) = H(X|Z \ | \ Y|Z) = H(X|Y \ | \ Z|Y)$ ?
If it is not true in general, then can one say anything particular when $X,Y,Z$ are Gaussians, and jointly Gaussian.