Dog's Chance Meaning

(idiomatic) little or not likelihood

Example: 2014, Ian Jack, "Is this the end of Britishness", The Guardian, 16 September 2014:
  One day, more than 60 years ago, we went as a family to the National Wallace Monument. My father took a binary, black-and-white approach to people and things: in toothpaste, Colgate was bad and Euthymol good; in bicycles, Raleigh was preferred to BSA; in Polar explorers, Captain Scott didn’t stand a dog’s chance against Amundsen.