If we're uncertain about the probability of an event *x *occurring (in virtue of the fact that *x *has occurred none or just a few times), how should we update our probability of *x *occurring in the future, in the face of *x *not occurring over a period of time?

(One example of *x* may be a nuclear war/accident.)

Sorry if this is very noobish.

This is one of those questions where there are a lot of possible answers depending on what model you have. It's a kind of order statistics/extreme values and model uncertainty question. So you could use Laplace's law of succession, you could use the hope function, you could try to fit some underlying continuous trend to predict binary outcomes or rates...