As the air temperature drops so does the ability of the air to contain water as a gas decreases. You need to understand the meaning of relative humidity. It is the percentage of the actual moisture present at a particular temperature relative to the saturation level at that temperature.
When the temperature of warm air decreases, because of the reduced water-holding capacity, there will be condensation of the excess water corresponding to the dew point. When that happens then the atmosphere is saturated and the RH is at 100%.
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