How does Shakespeare continue to hold out hope for Caesar at the beginning of Act Three? I don't know this question
In the beginning of Act III of the play, Julius Caesar, Shakespeare creates suspense by making some things happen that lead the reader to think perhaps the conspirators will not be successful in assassinating Caesar.
In the very beginning, Caesar notes to the soothsayer that the Ides of March are come (the soothsayer had previously warned Caesar to "Beware the Ides of March"). The soothsayer replies that yes, the Ides of March have come, but the day is not over yet.
Later, Cassius and Brutus fear that their plot has been discovered:
What said Popilius Lena?
He wish'd to-day our enterprise might thrive.
I fear our purpose is discovered.
Look, how he makes to Caesar; mark him.
Casca, be sudden, for we fear prevention.
Brutus, what shall be done? If this be known,
Cassius or Caesar never shall turn back,
For I will slay myself.
So here we are led to believe that the plot may not succeed.
Now, you try! Look at some of the other dialogue and see what you can find to answer your question. You can read the play online at the link below. See the analysis here on eNotes. Good luck!