Ambition is certainly one of the reason the conspirators kill Caesar, but it is not the only reason. You must look at the man to determine what he wants as a result of Caesar's death.
Cassius is the main instigator of the plot to kill Caesar. He uses Caesar's ambition as an excuse for his murder, but Cassius never gives any proof of Caesar's ambitious nature. All Cassius does when he tries to convince Brutus to join his plot is give Caesar's weaknesses. Primarily, Cassius is jealous of Caesar and resents his popularity.
Brutus must be convinced by Cassius to join the conspiracy. Brutus is idealistic and firmly believes in a republican government. He's afraid that Caesar is so popular, the people will make him king. Brutus is considered a noble man who wants what is best for his country.
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why is Caesar picked to be king?