██ - Original Distribution
██ - Forget Table Distribution
Above is a Gaussian distribution being decayed as it would in forget table. At every iteration of the decay algorithm, each bin decays a certain number of elements, as given by a Poisson process, and the distribution is renormalized. This is visualized side-by-side with the original distribution for comparison.
As you can see, this first "forgets" the less probable bins, ie: the tails of the distribution, thus putting more weight on the more probable events. As the decay continues, the distribution slowly approaches uniformity.
If we were to also have the distribution be non-stationary (ie: update the distribution with new observations as the decay process is happening), the decayed distribution would more closely show recent probabilities. As a result, the decaying distribution shows us what we believe the probabilities on our bins are considering recent data.