A probability, not a share of the day
A 40% value means the forecast system estimates a 40% chance of measurable precipitation at the specified point during the stated period. It does not mean rain for 40% of the day or over exactly 40% of a city.
The period matters. A 40% hourly probability differs from a 40% daily figure because the daily value summarises a longer window with several possible time steps.
It does not describe intensity
A low probability may accompany an intense but highly local shower, while a high probability can concern light, persistent rain. Read it together with expected millimetres, duration and thunderstorm information.
For an outdoor activity, recent observations and radar become more useful as the time approaches. Probability alone is not enough for a safety decision.
Why the percentage changes
New observations and changing model solutions can shift precipitation bands. For small-scale convection, a displacement of only a few kilometres may substantially change the probability at one location.
Treat the value as a measure of uncertainty and combine it with amount, timing and precipitation type rather than reducing the forecast to a simple yes or no.
This guide is educational. For safety-critical decisions, use current observations and follow the competent official authorities.