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As you have now learned, being broody does not require the presence of a rooster, fertile eggs or even eggs at all -- it is a hormonal condition that can strike a hen at any time whether or not there is any hope of it coming to fruition.
Left to her own devices, it is unlikely that her broody state of mind will break any time soon and since the process is hard on a hen and detrimental to your egg production when there is no hope of hatching eggs it is better for all involved to break the broodiness. This can be easily accomplished and there are several methods (search break broody here on BYC) but I prefer the "broody buster" which is a wire bottom cage that is located in an elevated position to allow for air flow from underneath -- the hen, food and water go into the cage (no bedding) and she is left for a few days. At the end of the initial period you release the hen to see if she has snapped out of it or goes back to brooding -- if she is still feeling broody she goes back in the cage for a few more days.