Alone with Claudius, Laertes asks why Claudius didn't punish Hamlet for killing Polonius. Claudius answers: First, he loves Gertrude and she's Hamlet's mother; second, Hamlet is loved by the people, so punishing him might have caused a revolt.
Claudius is always calculating, always careful to manipulate events and perceptions of events. He has already blunted Laertes' purpose.
A messenger enters with letters from Hamlet. Claudius is bewildered at Hamlet's return. Laertes is pleased: now he'll get his chance at revenge. Claudius comes up with a plot. Claudius says Laertes' skill with a sword recently aroused Hamlet's envy, and Claudius thinks they could lure Hamlet into a duel with Laertes. Claudius asks to what length Laertes would go to get revenge on Hamlet. Laertes says: "to cut his throat in a church" (4.7.98).
Claudius uses flattery of Laertes swordsmanship to convince Laertes to join his plot. Claudius doesn't care about Laertes' honor. He just wants to get rid of Hamlet. Compare Laertes willingness to kill Hamlet in church; this is exactly what Hamlet refused to do to Claudius.
Claudius reveals his plan: they will poison Laertes's sword. The slightest scratch will kill Hamlet. As a backup, Claudius decides to poison a glass of wine and offer it to Hamlet during the duel.
Laertes, who prides himself on honor, has been corrupted. He's joined an ignoble plot using deception and poison.
Gertrude rushes in with news that Ophelia has drowned. While gathering flowers she fell into the river and sang songs as her clothes grew heavy and pulled her under.
The male response to tragedy is to seek revenge. Ophelia, who cannot "act" because she's a woman, opts for suicide.
Laertes, weeping, exits. Claudius fears Ophelia's death might reignite Laertes anger and rebellion. He and Gertrude follow Laertes to calm him down.
Claudius only cares about how Ophelia's death might affect him and his power.