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Herod was himself a king of Arabia under the name Obodes II, king of Mauretania/Numibia under the name Jubba II, and king of Parthia under the name of Phraates IV.
The three kings or wise men/magi would have corresponded to three princes under Herod himself that were designated as rulers in various regions under his power. For example, by the time of Jesus' birth Herod had already named Aretes IV as his successor in Nabataea/Petra. (Aretes IV likely corresponds to Herod's brother-in-law/nephew Costobarus, the Roman consul of 16 BC, L. Domitius Ahenobarbus).
The Magi bow to Jesus, because he had been designated as the future heir of Herod the Great, and therefore a "king of kings" within the empire.
© Charles N. Pope, US Library of Congress. All rights reserved.