The initial chance of survival, after hearing that there is a chance, (for Prisoner A) is 1/3, since any one prisoner dies out of three. If he now knows, after

The initial chance of survival, after hearing that there is a chance, (for Prisoner A) is 1/3, since any one prisoner dies out of three. If he now knows, after consulting with the guard, that Prisoner B is sure to die that means that it's death for either A or C. Hence the chance of survival (and death since P(Death) = 1 - P(Survival)) is now 0.5. This results in a smaller chance of death (for him) 1/2 rather than 2/3. Hence the rejoicing.