If the chances for win are accurate (from the Premier League on Google), which are as follows for each of the three:
Liverpool: 63%
Man City: 77%
Arsenal: 83%
Then it's actually more likely than not, that at least one of these three won't win their game (around 60% probability).
Of course, it's hard to put an accurate number on sports events, it's all just estimates mostly based on previous results.
It's a big joke, bookie is more accurate because the statistic comes from people who want to bet and they as a bookie, won't make a mistake to calculate the odds, otherwise they will get rekt.
Arsenal is rarely become a champion and they're currently not on top standings, so there's no way to predict Arsenal has a bigger chance among other clubs.
