Conversation so far:
Did Claudius assassinate Caligula?
There is no evidence that Claudius had a direct hand in the assassination.
How was Claudius involved?
although it has been argued that he knew about the plot -- particularly since he left the scene of the crime shortly before his nephew was murdered.

Question: What happened after the murder?
Self-contained rewrite: What happened to Claudius after the murder of Caligula?