Most quests are started with little chance that they will succeed; we usually only hear about the ones that are successful. When Thingol gave Beren his quest to retrieve the Silmaril from Morgoth's crown, he thought it was a surefire way of ridding a strong suitor from the life of his daughter, L’thien.

Same when Elrond said Aragorn could only wed Arwen when he became King over both Arnor and Gondor.

Finally, who in their right mind would believe a couple of hobbits could break into Mordor and toss Sauron's prize possession down the fiery tube right under the enemy's nose, or eye, as it were.