Hume: Liberty

Hume's discussion of liberty is not as detailed as his discussion of necessity. That bothers me because I agree with everything he says about necessity, but I'm unsure of some of the things he says about liberty. His general description of liberty is that person P is at liberty with respect to performing a certain act A if and only if, if P were to choose to do A then he would be able to do A. Although this seems to give a satisfactory explanation for freewill, I think that Hume is restricting himself. In this definition, he is not presenting P with a choice--there is only act A. What if P had to make a decision between A and B, and he can only choose one even though he wants to do both. If he chooses A, then how do we know that he was at liberty to choose and perform B (or even that he was at liberty to choose and perform A)? We cannot affirm that he chose A because he was at liberty to do so unless we send him back in time and see if he can choose B in the exact same moment and situation. Otherwise, it is just as possible that he chose A because all of the facts about the world and the laws of nature determined that he would choose A at that time and in that situation. Although liberty sounds like a nice thing to believe, I am always pushed towards thinking it isn't true for reasons like this.