If I have $X$ and $Y$ discrete r.v.'s with outcomes $\{x_1,x_2\}$ and $\{y_1,y_2\}$ and entropies $H(X)$ and $H(Y)$. Let $P_{x|y}(x_1|y_1)=P_{x|y}(x_2,y_2)=0$. Prove that $H(X) = H(Y)$ (entropy theory).
If I come up with example numbers and assign that to variables that will prove it. But I need formal way to prove it.
Thanks in advance!