I think to imagine that P is impossible is to imagine a being experiencing frustration trying to bring P about.
I would like to give an anti-realist account of modality in terms of this, but I think analogs to Crispin Wright’s ("Truth and Objectivity") argument that coincident normative force (his example, P’s truth and P’s warranted assertibility) does not guarantee even coextension, and my arguments in my paper about Moore’s Paradox can be applied here. Wright’s argument can be responded to by using intuitionist logic (the bad consequence is not so bad when stated in intuitionistic logic). My argument can maybe be responded to with Dubuqc’s feasibilism.
In addition, it might be too circular to analyze P’s possibility in terms of the possibility of an agent bringing it about that P. I think that our experience of frustration is an actual, occurent experience though. I don’t know if this is enough though.
Next semester I’m teaching John Divers book "Possible Worlds," in the hope that I can get clearer about this.