诈姐，人民群众的眼睛是雪亮的，忽悠只有死路一条。

假设有三个门A，B和C，lucky door是其中的一个，被选中的prob=1/3。假设你的initial selection是A，then

lucky door door opened
A B*
A C* *each with equal probability = 0.5
B C
C B

Using the table above, we can calculate
P(B)
=P(B opened)
=P(A is the lucky door and B opened)+P(C is the lucky door and B opened)+P(B is the lucky and B opened)
=1/3*1/2+1/3+0
=1/2

So
P(A|B)
=P(A is the lucky door|B opened)
=P(A is the lucky door and B opened)/P(B opened)
=(1/2*1/3)/(1/2)
=1/3