I am trying to deduce the following formula, from "Information-Theoretically Secure Secret-Key Agreement by NOT Authenticated Public Discussion" (Definition 4, page 9):
$P_{\tilde{X}Y}(x,y) = \sum_{x'}\sum_{z}P_{XYZ}(x',y,z) \cdot P_{\tilde{X}|Z}(x,z)$
but can't figure it out. Probably (among other things), what is puzzling me is the $\tilde{X}|Z$ inside the summatory since, on the one hand, the summatory does not iterate over $\tilde{X}$, yet it deals with the conditioned probability of $\tilde{X}$ given $Z$ (and something similar for $Y$).