Hamlet is already under intense scrutiny by Claudius, who suspects that his stepson is plotting against him. Claudius will be watching and analyzing Hamlet throughout the play, and he will use others to help him pry into his stepson's soul. In a beautiful metaphor he tells Polonius
There's something in his soul,
O'er which his melancholy sits on brood,
And I do doubt the hatch and the disclose
Will be some danger...
Notably, he sends for Rosencrantz and Guildenstern, Hamlet's old school friends, to ask the prince leading questions and try to learn his secret thoughts. Claudius also uses Polonius to question Hamlet, and Polonius uses Ophelia for a similar purpose. Claudius also tries to use Gertrude for that purpose, especially in the scene in which Polonius is hiding behind the arras.
After his meeting with the ghost of his father, Hamlet understands that he is going to have to be even more careful...
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