From Longman Dictionary of Contemporary Englishdefy logic/the odds etcdefy logic/the odds etcto not happen according to the principles you would expect a 16-week premature baby who defied the odds and survived → defy
Examples from the Corpus
defy logic/the odds etc• That Jaime Guerrero is alive to attend the dinner probably defies the odds.• In the event, the cyclist defied the odds and survived. 