slotted aloha probability problem

Hello.
I'd be very glad if someone could help me with the following question.

607 stations divided into two sets. The first set contains 100 stations, whose maximal distance is 1,000 km, and the second set contains the remaining stations, whose maximal distance is also 1,000 km. Each set will communicate between its stations using slotted ALOHA (bandwidth =100kbps, frame = 2000 bits) and a different frequency. Frames that need sending between the first set to the second (or the other way around), will be sent via a special station which happens to be on both sets (and has infinite memory). These frames will be sent once to the special station, which will then send it on the second network. Assuming all stations introduce frames with the same probability, and that the recipient is also distributed with equal probability among all stations, what is the throughput of the new
system?

Throughput S is defined as : S = GP
where G is transmission-attempts per slot-time(this I think I can find) and P is the probability of successful transmission of a frame in a network.
The problem for me is to define P for the given system. Because , as far as i see, there are three cases: frame might pass within first set, frame might pass within second set and frame might pass between sets.
I tried to define P using conditional probability but lost my way a bit.

Will be grateful for any help.
Thanks .