That's not how it works. Probability of precipitation means exactly what it sounds like: the probability that precipitation will fall in a specific forecast area.
Interesting. The way I explained it was how it was explained to me by a group of weather forecasters. For instance, here [0], is an explanation from a random weatherman that is in-line with how I was told.
[0] https://www.ktvh.com/news/weather-wise/weather-wise-so-there...