From the problem statement “on any given day”, the probability of a forecast for rain was 0.2.
The occurrence of an event does not alter the probability of its occurrence. Even on a day with “no rain” forecast it is still possible for it to actually rain. That event only means that a low-probability event occurred. It does not change the basis of the prior probability.
Therefore, if on “any given day” the probability of a “rain” forecast is 0.2, then on that day also, the forecast probability for rain must have been 0.2.