Gur Huberman points us to this page from the National Weather Service, “Explaining ‘Probability of Precipitation,’” which says:
Probability of Precipitation = C x A where “C” = the confidence that precipitation will occur somewhere in the forecast area, and where “A” = the percent of the area that will receive measureable precipitation, if it occurs at all. . . . the correct way to interpret the forecast is: there is a 40 percent chance that rain will occur at any given point in the area.
So now you know.