Answer: The king believed that his son had drowned.
Explanation:
We have learned previously through Prospero and the familiar spirit that is, Ariel’s conversation, that it was Ariel who caused the tempest which struck the ship transporting Alonso, Gonzalo, Sebastian, Ferdinand, Antonio, Stephano, and Trinculo, by making sure that they got safely to the island but that they were divided into small groups.
On another part of the island, Sebastian, Antonio, Alonso, Gonzalo, and other lords were giving thanks for their safety but were worrier about the fate of Ferdinand.
Alonso ended up in a group that had Gonzalo, Sebastian, Antonio, and they were afraid that Ferdinand may have been drowned. This made Alonso regrets marrying his daughter which was the reason they made the sea journey.