Looking on the internet deeply has found these results:

They can win the race. is the most popular phrase on the web.

They could win the race yesterday. 10 results on the web	They can win the race. 1652 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	if persuaded to run. Bill Salisbury. Four decades after the election that shattered the glass ... meaning they could be a ... Minnesota Capitol: Women have proved they can win the race Jan 19, 2015 ... ... people with their cars in order to acquire points so that they can win the race ( never mind actually getting first place in the actual race itself). ... place where speed is especially important. During a race, the snowmobiles in the track cover the distance in as little time as possible, so they can win the race. Sep 24, 2014 ... As focused as they are on making sure they can win the race, the two know that they'll be able to work well as a team

They could win the race yesterday.

10 results on the web

They can win the race.

1652 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

if persuaded to run. Bill Salisbury. Four decades after the election that shattered the glass ...
meaning they could be a ...
Minnesota Capitol: Women have proved they can win the race
Jan 19, 2015 ... ... people with their cars in order to acquire points so that they can win the race ( never mind actually getting first place in the actual race itself).
... place where speed is especially important. During a race, the snowmobiles in the track cover the distance in as little time as possible, so they can win the race.
Sep 24, 2014 ... As focused as they are on making sure they can win the race, the two know that they'll be able to work well as a team