"Probability of rain" forecast meaning

Please help me understand the "precipitation probability" commonly listed hour-by-hour in weather forecasts.

For example, the hour by hour forecast for Manhattan NY today includes probabilities of precipitation:

1pm 2%
2pm 2%
3pm 2%
4pm 2%
5pm 2%

(additional probabilities for other hours are also listed)

For the whole day, however, the forecast precipitation is only 3%.

How does this makes sense?
What is the probability of precipitation for a one hour period?
What is the probability of precipitation for a three hour period?


Forecast source:
https://www.wunderground.com/hourly/us/ny/manhattan/40.75,-74.00

 

this link might help you
https://www.wesh.com/article/what-does-a-chance-of-rain-really-mean/4440726

 

When a weather forecast says "there is a x% chance of rain", what it means is "out of all of the times in the past when weather conditions were like today, it rained x% of them."