Well, the damage is already done. Luthier time it is. In future, never pluck out a broken hair. Instead, cut it off at both sides with scissors (or a nail clipper, something that fits in the violin case), close to its start/end. What keeps the hairs fixed is the bulk of the other hairs wedged in with them, so you don't want to remove the ends of the broken hair even if you could do it without moving the others.
If it breaks while playing, you can usually ignore it for the movement and try breaking the long end by pulling between both hands (so that you don't pull at its bow attachment). Horse tail hairs are rather strong, so don't bank on success here. And don't try helping with fire. If you are unlucky and the whole bow conflagrates, you have more of a problem than you started with.