against all odds
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.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.
Examples from the Web for against all odds
And talk about an against-all-odds romance: for years it seemed as though nothing could keep Hunter and Edwards apart.What You Can Learn From John Edwards and Rielle Hunter
June 27, 2012