Could the cup's water leak out?
From the conclusion, the water on the surface of the cup is derived from the air. In an arid desert, dew does not occur.
If you put the ice in the cup, the cup's surface becomes cloudy after a while because the water vapor in the air condenses and becomes droplets.
When the temperature decreases, the amount of water vapor that can be contained in the air is reduced, and some water vapor condenses and becomes water.
The temperature at which water vapor begins to condense is called the dew point.