The water on the outside of the glass did not come from inside the glass, it came from the atmosphere. The amount of water vapor that the atmosphere can hold increases as the temperature increases. The outer surface of the glass has been cooled by the iced beverage inside. When air comes into contact with this cooled surface water vapor in the air will condense onto the surface if the air contains more water vapor than it can hold at the new lower temperature. This is more pronounced when the humidity is higher.
This is how dew forms. When the air cools overnight it's no longer able to hold as much water. The temperature at which water vapor will begin to condense depends on the relative humidity and is called the dew point.