Global warming is expected to increase global mean precipitation by 2-4%/K, but this increase may be very uneven, leading to more flooding but also droughts. Utilizing the Gini index, a metric frequently used in economics, we analyze the unevenness of precipitation distribution locally and globally from daily to annual-mean timescale in CMIP6 global warming simulations. The unevenness of daily precipitation increases in all models over land and ocean, tropics and extratropics. Local-daily precipitation unevenness changes show a complex geographic pattern. However, particularly over land, we show that a simple theoretical scaling explains this complexity to result from increased precipitation intensity scaling at about the Clausius-Clapeyron rate, and a local balance between changes in time-mean precipitation and dry-day fraction. These results provide a novel perspective on the relation between global constraints on hydrological cycle to regional precipitation changes independent of changes in the quasi-stationary atmospheric circulation and geographic distribution of precipitation.