Please help me calculate this probability

Hi.

I'm struggling to get my head round this issue I'm discussing with friends.

It regards the chances of any of the top 4 teams from last season in a league playing each other on the same day.

So, assuming 20 teams (they play twice, home and away) who each play on the same day once a week for 38 weeks, what is the chance that the teams who finished in positions 1-4 last season, will play each other on the same day at any point in the season given a random fixture draw.

I've been told 17% but that seems too low to me.

Can anyone explain how this would be calculated?

Thanks.