Searching for that lost key in the dark is a fool's errand.
fool's errand
idiomA foolish undertaking, especially one that is purposeless, fruitless, nonsensical, or certain to fail.
Origin
disputed originFirst use apppears c. the 18th century.
Trying to fix this broken computer without any tools is just a fool's errand.
The explorers realized that searching for the mythical city in such harsh conditions was a fool's errand, yet they continued their journey regardless.