Use it when someone has won by a large margin and there's no doubt about their victory. In the race, Sarah was no contest; she finished minutes before anyone else.
Pro Tip 2/3
Non-Competitive
Describes a situation where there is no real competition due to obvious difference in skill or ability. His chess skills are no contest against the grandmaster.
Pro Tip 3/3
Figurative Use
Can be used metaphorically to express an easy victory in any comparison, not just physical competitions. Choosing between the two restaurants was no contest; the new one is far superior.