Since you are in a state of ignorance with respect to \(X\), your representor contains probabilities that take \(Y\) to be good evidence that \(H\) and probabilities that take \(Y\) to be good evidence that \(\neg H\). So, despite the fact that \(P(H)=\{1/2\}\) we have \(P(H\mid Y) = [0,1]\). This phenomenon—posteriors being wider than their priors—is known as dilation. The phenomenon has been thoroughly investigated in the mathematical literature (Walley 1991; Seidenfeld and Wasserman 1993; Herron, Seidenfeld, and Wasserman 1994; Pedersen and Wheeler 2014). Levi and Seidenfeld reported an example of dilation to Good following Good (1967). Good mentioned this correspondence in his follow up paper (Good 1974). Recent interest in dilation in the philosophical community has been generated by White’s paper (White 2010).