Most places I look at report both probability and give a measurement prediction.

So it would be like "60% chance of rain after 2pm, total amount less than 1/10th of an inch"

Meteoswiss has timeserie histogram with of amount of rain with confidence intervals (10th and 90th quantile)

It tells you all you need to know at a glance :)

e.g. see https://www.meteoswiss.admin.ch/images/1904/website/weather/...

(from https://www.meteoswiss.admin.ch/weather/weather-and-climate-...)