Box 1 contains 2 red marbles, box 2 contains 1 red and 1 blue marbles, box 3 contains 2 blue marbles.?

We are given the condition that a blue marble was picked, so that eliminates the case that box 1 was picked.

There are 3 ways to pick a blue marble.
1) Pick box 2 and pick the blue marble
2) Pick box 3 and pick the first blue marble.
3) Pick box 3 and pick the second blue marble.

In 2 of these 3 cases, the remaining unpicked marble is also blue.

Answer:
2/3

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If a blue marble is picked, then either box 2 or box 3 was picked otherwise a blue marble could not have been picked. The probability that the other marble is blue is zero if box 2 was picked and 100% if box 3 was picked.

Given that a blue marble was picked the probability the other marble in the box is also blue is :
(1/2)(0) + (1/2)(1) = 50%

P(box1) = 0 ... the first marble selected IS blue, and ut has no blue marbles
... so either box 2 or box 3 has been selected
box 2 .. order of marbles would be B then R
Box 3 .. order of marbles would be B then B ... 2 possibilities with one being successful
so the prob. = 1/2