Last Marble Standing

An urn contains $r$ red marbles, $b$ blue marbles, and $g$ green marbles. You draw marbles one at a time, uniformly at random, without replacement. What is the probability that immediately after the last red marble is drawn, there is still at least one blue marble AND at least one green marble remaining in the urn? Derive a general formula, then evaluate it for $r = 10$, $b = 20$, $g = 30$.