I was close but forgot how to add. The correct answer is 1/3 chance of surviving if he stays, and 2/3 chance of surviving if he changes. P + Q = 1.
Final answer.
We all agree that he has a 1/3 chance at the beginning, if he stays in A. That doesn't change. And a 2/3 chance for the other two cells. When the warden breaks the news about his buddy in B, this stuff doesn't change. It does mean however that this 2/3 chance now resides only in B.