illness?

Claudius is very skeptical of Hamlet and whether he is faking his illness, or if it is for real. However, I tend to believe that Claudius does think that Hamlet is truly mad. At the end of act III.i the king and polonius were disscusing the meeting between Ophelia and Hamlet. The king mentioned that what hamlet had said didnt really make sence and his thought process was distorted. With this the king desired to send Hamlet away to England; this is evident when he said, "It shall be so. Madness in great ones must not unwatched go".