Fog is actually not a form of precipitation, but of condensation. 
How Condensation Works
Condensation is the process by which water vapor turns into a liquid. This can happen when the air is cooled to its “dew point” – the temperature at which condensation occurs. When the air becomes cooler than the dew point, it is unable to maintain the high amount of water vapor. 
What Is Fog?
Fog is defined as miniscule water droplets suspended in the air that produce a cloud layer in contact with the ground reducing horizontal visibility to less than 1,000 meters. If visibility is greater, the occurrence is called mist or haze depending on whether it’s caused by solid particles or water droplets. 
How Fog Works
Fog forms when the relative humidity of the surrounding air surpasses 100 percent. How this condensation occurs depends on the type of fog. The condensation that causes radiation fog is due to reduction in the Earth’s surface temperature. When the Earth begins to cool at nightfall, the heat that the surface absorbed during the day begins to radiate upward. If there is a deep enough layer of moist air near the Earth’s surface the relative humidity will surpass 100 percent when condensation will occur and fog will result. Advection fog occurs from the condensation that results from warm moist air floating over a cold surface such as the fog that you see at the ocean. Upslope fog results from winds blowing warm moist air up to a colder higher elevation such as the side of a mountain. The condensation from evaporation fog occurs when evaporation causes moist air to mix with cooler, dry air. A common form of evaporation fog is steam fog that appears as ‘smoke’ coming from the surface of water. 
Why Isn’t Fog a Form of Precipitation?
For fog to be considered a form of precipitation, it would have to be falling. As mentioned previously, fog is when water droplets begin to form, but are still lighter than air. Precipitation occurs when the combined water molecules caused by condensation become too heavy to float in the air, leaving them nowhere to go but down. 
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