The probability of pulling a green marble on the first draw is 5/19.
After removing a green marble, the probability of pulling a green marble on the second draw is 4/18.
Lastly, the probability of pulling a green marble on the third draw is 3/17.
So, the probability of pulling all green marbles is (5/19) * (4/18) * (3/17) = 60/581.
Therefore, the probability is 60/581.