It does become P2. But… aside from the submarine issue… if you play Russian Roulette against one other person, then with probability 1⁄2, the other person gets shot before you do. Assuming that the loser either dies or is incapacitated, we can write P1 as Pr[survive|shot] and P2 as Pr[shot|survive], and by a simple application of Bayes P2 is at most twice P1.
It does become P2. But… aside from the submarine issue… if you play Russian Roulette against one other person, then with probability 1⁄2, the other person gets shot before you do. Assuming that the loser either dies or is incapacitated, we can write P1 as Pr[survive|shot] and P2 as Pr[shot|survive], and by a simple application of Bayes P2 is at most twice P1.