From Longman Dictionary of Contemporary Englishout of thin airout of thin airout of nowhere, as if by magic It seems like researchers have just pulled the numbers out of thin air. → thin
Examples from the Corpus
out of thin air• The juice landed on the floor like a red bubbly snake, a bad omen suddenly materializing out of thin air.• Ray picks a number out of thin air -- generally below wholesale -- and the deal is done.• He found rhymes irresistible, and produced them out of thin air, just for the fun of it. 