[SCfuji]

Your friend asks you to guess a number between 1 and 3. You tentatively guess 1, and your friend tells you the number is not 2 (intentionally choosing one of the numbers you did not guess). The chances that the number is 3 are then 2/3.

Friend A asks you to guess a number between 1 and 3. You and Friend B work out a plan for you to initially choose 1, while Friend B guesses either 2 or 3 in order to take advantage of the above probability. Friend B guesses 2, and Friend A tells Friend B that he is wrong. Now the chances that the number is 3 are 1/2.
Explain.