They're not equally probable. The probability depends on latency to the pool and mining speed. All that's necessary to prove that a pool is not hop proof is to show that there exists some time an attacker can identify where the payout is greater than the payout from solo mining. The claim is that the payout method is mathematically proven to be hop proof. That seems impossible, again, unless I misunderstand the method.

All that's needed is for my latency and mining rate to be sufficiently good that the reward I expect for my first share if I don't find a block outweighs the risk that someone else will submit a share before I find my first share. If I understand this method correctly, it cannot be mathematically proven to be hop proof because you have to make assumptions about latency and mining rate.