The key here is something called a Dynamic Equilibrium - a common concept in my field, Physical Chemistry. To keep it simpler, let's deal with the particular situation posed by OP, but in stages.
First, assume we have a closed container (jar with lid on it) containing some dry rice grains, air, and a small mount of water molecules (vapour) in the air, as normally happens. Now the starch molecules of the rice grains have a chemical structure that is very attractive to water molecules, so some of those water molecules in the air will attach themselves to the starch rather firmly and stay there. This decreases the concentration of water molecules remaining in the air, so it's a little harder for the starch to acquire more of them. But some still do attach to the starch, AND at the same time, some that are already attached, detach and return to the air. At some point, we achieve a state of Dynamic Equilibium in which the rate of water molecules leaving the air and attaching to starch (rice grain) surfaces exactly matches the rate of the reverse - the water molecules that leave the starch surface and fly off into free air. At this point, the concentration of water molecules in the air is lower that it would be in plain room air, because the starch (rice grains) with their special affinity for water molecules has "stolen" them from the air. This is how ALL desiccants work. They don't just keep something dry - they do it by selectively absorbing water from the trapped air in a closed container, thus drying the air. (Any desiccant, including rice grains, has a limit on how much it can absorb. But for this case we are assuming that there is much more rice present that water vapour, and that limit is not a problem.)
Now, assume that someone temporarily opens the jar and places a few droplets of liquid water on the inside of the jar, then closes the lid. We now have a new second system operating - the system of dry air surrounding liquid water droplets. Some of the water will evaporate, increasing the water molecule concentration in the air, and reducing the amount of water in liquid form. If there were nothing else operating in the jar, eventually a new Dynamic Equilibrium would be established in which the rate of evaporation of liquid water into the air is exactly equal to the rate of condensation of water molecules out of the air into a liquid form on the jar's wall. But wait! We have water-hungry rice grains sitting in the bottom! That Dynamic Equilibrium system is also working to remove water molecules from the air and tie them up on the starch surfaces. So the combined effect is to move water liquid molecules into water gaseous molecules in the air, and then to remove them from the air by attachment to the starch (rice grain) surfaces. It is an overall Dynamic Equilibrium composed of two sub-processes, and using the air in the jar as a transport medium to move the water from liquid droplets into individual molecules flying around in the air until they become attached to the rice grains. As long as there is enough dry rice to make sure there are still large numbers of starch surface sites anxious to absorb water molecules, the result will be that ALL the liquid water gets evaporated from the jar walls so they are dry, and the air in the jar is still quite dry. Thus, this system will "dry up" all the liquid water, given a bit of time for the processes to proceed.
Third scenario: the water droplets are not placed inside the jar wall by a person. Instead, a circuit board with liquid water trapped in crevices is placed inside the closed jar. Exactly the same process occurs. Liquid water evaporates into the surrounding air through the tiny crevices and floats around in the jar as individual molecules until they get trapped on the rice grain surfaces. After a while, all the liquid water had been removed from the circuit board, and it is truly dry.
A fan in an open space and blowing over the damp circuit board will dry things out by removing any air that contains excess evaporated water molecules and supplying fresh air. As long as that fresh air is dry, it will encourage further evaporation (drying) of liquid water from the crevices. The dryer the air, the faster you can dry out the circuit board. And of course, the faster the air flow, the faster it will dry.
Inside a closed jar with a desiccant (like rice grains), the air is VERY dry and that speeds up the process, BUT the air flow velocity is low. If you had a container for rice and circuit board that also had space for a small circulating fan inside, that would be ideal! You would NOT want a supply of outside fresh air. All the fan is doing in this case is speeding up the flow of air (dried continuously by the rice) to enhance the process.