Q: You enter a town that has K killers and P pacifists. When a pacifist meets a pacifist, nothing happens. When a pacifist meets a killer, the pacifist is killed. When two killers meet, both die. Assume meetings always occur between exactly two persons and the pairs involved are completely random. What are your odds of survival?

A: Regardless of whether you are a pacifist or a killer, you may disregard all events in which a pacifist other than yourself is involved and consider only events in which you are killed or a pair of killers other than yourself is killed.

Thus we may assume that there are N killers and yourself. If N is odd, your odds of surviving are zero. If N is even, it doesn't matter to you whether you are a killer or not. So WLOG assume you are. Then your probability of survival is 1/(N+1).