It is likely that the forecast is made using an ensemble of runs from a weather model. As weather is chaotic (deterministic, but heavily dependent on initial conditions), each run will show a different pattern of precipitation, and the probability is likely to be simply the proportion of model runs that exhibited precipitation in that location during that hour. Sometimes the pattern in each model will be very similar (e.g. a weather front going through) or they may be very different (AIUI convective rainfall, e.g. thunderstoms, are less predictable, so each run may have a broad pattern of isolated showers, but you will miss them in some runs but not in others).
Note that "location" will mean the grid box in the weather model (km^2?), it doesn't mean that it will rain everywhere in that grid box, and definitely not a cup. I used to play cricket quite regularly at a place with three cricket pitches all within sight of eachother. I can remember several occasions where it was raining on one pitch, but not another (play stopped on one pitch but carried on on the other).