against all odds | against all the odds

Meaning: If you do something against all odds, or against all the odds, you do it even though there were many problems and it didn't seem possible to do.

For example:

• He had a serious accident and was close to death but, against all odds, he recovered and now he's fine.
  
• No-one thought we could do it but, against all the odds, we won the Olympic gold medal.