Estimate rain likelihood from conditions.
Rain needs moisture, saturation and lift. Humidity and the temperature-dew point spread measure how close the air is to condensing, cloud cover confirms it is already happening aloft, and a falling barometer is the signature of the lift that turns cloud into precipitation. Scoring each factor separately shows which one is carrying the forecast, and a rapidly falling pressure also shortens the expected time to onset.
Rain likelihood score
Probability = (RH - 55) x 0.9 + (30 - spread x 4) + cloud/100 x 20 + (-pressure change x 3), each component capped
High humidity with a small dew point spread, thickening cloud and a falling barometer together are the classic combination. Any one alone is much weaker evidence.
Falling pressure marks an approaching low or front, where air is rising. Rising air cools and condenses, which is the mechanism that produces precipitation.
No. Numerical weather prediction uses full atmospheric physics; this is a local rule-of-thumb assessment from conditions you can observe yourself.