To what degree does Claudius know Hamlet as a threat?

Claudius knows that there is something more behind Hamlet's madness besides his sadness over his father's death and anguish over his mother remarrying so soon. This is evident because Claudius is so concerned with Hamlet's madness, when he doesn't even like Hamlet. This suggests that Claudius is watching Hamlet closely, to see if his anguish is caused by his knowledge of something he shouldn't know (King Hamlet's death). Even when national matters come up, such as in Act 2 scene 2 in lines 50-53, Claudius does not care about anything but news of Hamlet's madness. I feel that Claudius knows that Hamlet knows something, but he's not sure what it is, or to what extent. Currently he's just carefully observing, and letting Polonius's efforts do the work for him in terms of spying, and trying to figure Hamlet out. I guess one could say Claudius is on the defensive right now.