The problem is that the weather forecast does not focus solely on the roughly four square foot area you’re standing in, but rather, a much larger area enclosing hundreds of square miles. And while it may rain in one part of that area, it does not necessarily rain throughout the whole area. So the formula for “chance of rain” — or, more accurately (and officially) “probability of precipitation” — has to account for this. So there’s a formula, as the National Weather Service explains: P = C x A.
Read his entire newsletter on the topic because it is very informative.