Rain chances are always given for a long period, like “today” or “tonight”, but what is the chance at any given moment? It rarely rains for an entire 24-hour day, so the chance of rain at a given time must be less than the chance during an entire day.
A computer search through 147 years of Chicago precipitation records, 1871-2017, reveals that the chance of measurable rain or snow in a full 24-hour day is one in three: 33 percent. But as you point out, precipitation is often of short duration even on a “wet” day.
The chance of experiencing precipitation at any given moment is another matter entirely. An in-house study of the precise times during which precipitation was actually falling at Chicago for all days during the years 2002-2016 yields four percent. The chance of you getting wet at any given moment is only four percent.