Why did prospreo lose his dukedom?

Prospero lost his dukedom because his brother, Antonio, conspired against him and usurped his position as Duke of Milan. While Prospero was preoccupied with his studies in magic, Antonio seized power with the support of the King of Naples, ultimately banishing Prospero and his infant daughter, Miranda, to a remote island. This betrayal set the stage for the events of Shakespeare's "The Tempest," where Prospero seeks revenge and reconciliation.