1
general::
Phrase(s): against all odds
despite very low probability; in a most unlikely way. • Against all odds, she managed to win the trophy.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
In spite of seeming very unlikely, as in Against all odds we had a snowstorm in early May, or Against all odds the slower team won. This transfer of a betting term to general usage occurred about 1900.
American Heritage Idioms