Final answer:
The belief that Priam thought Hector would beat Achilles is speculative, as the texts provided discuss different aspects of the Trojan War and do not directly state Priam's beliefs on this matter. However, classical knowledge tells us that Hector is killed by Achilles in Homer's Iliad.
Step-by-step explanation:
The question relates to Priam's beliefs in the mythological context of the Trojan War as portrayed in Homer's Iliad. Since Priam is the king of Troy and Hector is his son, it's natural to think that Priam might have believed in Hector's victory, as any father might have faith in his son. However, the text provided does not specifically address Priam's belief in the outcome of the fight between Hector and Achilles.
Given the legendary prowess of Achilles, and the fact that he was dipped in the river Styx to make him invincible except for his heel, the odds were not in Hector's favor. Although Priam might have hoped for Hector to win, based on classical knowledge, Hector was indeed killed by Achilles, indicating that if Priam did believe Hector would win, his belief was not realized.