I arrived at answer in a simple way:

Say initial state of the bag is: R1 R2 R3 B1 B2 B3 B4

Imagine first marble removed is Red(R1).

The remaining is: R2 R3 B1 B2 B3 B4 = 6 marbles

Now I have to pick one more marble.

Total number outcomes = Number of permutations when I pick 1 marble from a set of 6 = P(6,1) = 6

We just want the probability of a blue marble coming in that experiment.

There are 4 possible favorable outcomes: B1,B2,B3,B4

So The probability of that outcome is = 4/6