Suppose it is an average value p, for the season.

At some other place there is an Indian chief who used to do the job for us for hundreds of years until such time as he was overtaken by modern technology and suppose he assigns the probability q to rain.

We know that the modern weather station is more reliable so we are likely to discard the value q and we say that p is correct.

But is that altogether true ?

Could it be that the correct probability in such situations is some function f(p,q) ? And if so how do we express it ?