He believes in some sort of coincidence, that is hopefully guided by something good rather than evil. He believes in it because he wants to, has to, else there is no hope for him.

He stares at the offered hand a moment and then to his dirt-stained ones, to see if she would mind, but he does wipe as much of it on his pants before taking her hand gently. "Frodo. I know someone named Rose too. Someone very important to my friend."