==> decision/prisoners.s <==
Each prisoner had an equal chance of being the one chosen to be
executed. So we have three cases:
Prisoner executed: A B C
Probability of this case: 1/3 1/3 1/3
Now, if A is to be executed, the warden will randomly choose either B or C,
and tell A that name. When B or C is the one to be executed, there is only
one prisoner other than A who will not be executed, and the warden will always
give that name. So now we have:
Prisoner executed: A A B C
Name given to A: B C C B
Probability: 1/6 1/6 1/3 1/3
We can calculate all this without knowing the warden's answer.
When he tells us B will not be executed, we eliminate the middle two
choices above. Now, among the two remaining cases, C is twice
as likely as A to be the one executed. Thus, the probability that
A will be executed is still 1/3, and C's chances are 2/3.