One has to suppose it was the lady behind the door. The princess would choose which door to direct him to based on his love for her. If he truly loved her, she could not bear to see him torn apart. If he did not love her, she could not bear to see him move on to some other woman. In his turn, he must recognize that there is some chance that she is lying to him, that she has chosen to send him to his death. Yet he turns towards the exact door she has directed him to with complete faith and calm. There is no doubt whatsoever in his mind that she has chosen to let him live. If he had been the conniving sort, he might assume that the indicated door was the one containing the beast, and on this basis selected the opposite door. Indeed, he is still offered a choice, between faith and deception, whether to do as she says, or to turn away from it. On this basis, one assumes, she would direct him towards the door of salvation, knowing that he might choose to ignore her, and turn towards the door of certain doom instead. (There is a parallel here to C S Lewis' description of religious faith, if you are familiar with his writing)