I do not understand how to set up this equation with regards to conditional probability.

In front of terminal 3 at San Francisco Airport is a pickup area where shuttles and taxis arrive according to a Poisson process. The shuttles arrive at a rate 11 = 1/20 (i.e. 1 shuttle per 20 minutes) and the taxis arrive at a rate k2 = 1/10 (i.e. 1 taxi per 10 minutes) starting at 00:00. The shuttles and the taxis arrive independently. ((1) Suppose you reach the pickup area at 00:20. You learn that you missed 3 taxis and 1 shuttle in those 20 minutes. What is the probability that you need to wait for more than 10 mins until either a shuttle or a taxi arrives