This is particularly problematic in areas of commplex terrain. Average point probability is not the same as areal probability. Areal probability is the chance of an event occuring in an area and is generally larger than the average point probability. As the areal size increases, the areal probability also tends to increase. For example, during the summer convective season the chance of rain at SLC airport is less than the chance of rain occuring somewhere in Salt Lake County which is less than the chance of rain occuring in the state of Utah.
Probability also tends to increase with the length of the time period.
Forecast skill is limited by lead time and as the lead time increases the forecast probability must converge on climatology. New forecasters tend to overestimate thier skill and use excessively high or low probabiliities. Consensus forecasts are generally better than most individual forecasts over long time periods. When Brier skill scores are used, changing MOS can be worth more at some probabilities than at others and in one direction more than the other. Westview Press, Boulder, Co. 545 pp.