if you think this in conditional probebility way:
P(A|B) = P(A&B)/P(B)
event A: the remaining marble from the same bag is also white
event B: the first picking marble is white
P(B) = 1/3*1 + 1/3*1/2 = 1/2
P(A&B) = 1/3 (the event A&B means that you must pick the "two white marble" bag, this happens with probability 1/3)
so P(A|B) = 2/3