The conspiracy to assassinate Caligula was a smashing success. But did the senate really wish to keep the Principate going? Why not go back to the republic? Well, the choice would be made for them; by the Praetorian Guard. For the first of many times, the right to rule the Roman Empire was simply purchased.
Primary sources Referenced:
Suetonius, Life of Claudius 3, 30.
Claudius Coin ('Emperor Received').
Claudius Coin ('Praetorians Received').
Cassius Dio, Roman History 60.3.2-3Buy Professor Elliott's newest book: Pox Romana: The Plague that Shook the Roman World, published by Princeton University Press.