In what ways does the quote "Success is somebody else's failure" apply to Julius Caesar?

You might want to think about this quote in relation to
the way in which power is shown to be grasped whenever there is a vacuum in the play.
The most notable example of this is Antony's transformation from a politician who is not
taken seriously to somebody who cynically uses the death of his former loved leader as a
podium to unleash the mob against the conspirators and ensure his own support. Surely
Antony is an excellent example of a Machiavellian politician, who sees the opportunity
to gain power through the death of Caesar and goes for it, transforming in a single Act
from a carefree politician to one that is able to chillingly discuss the murder of his
nephew and others to secure his position, even trying to turn Octavius against Lepidus
in Act IV scene 1:

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This is a slight unmeritable
man,

Meet to be sent on errands; is it
fit,

The threefold world divided, he should
stand

One of the three to share
it?

Antony definitely shows
how success is based on or built on somebody else's failure in this excellent tragedy
that has so much to say about the grasping nature of power.