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%
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.
I think this prediction is limited to their next match, not to who will win the Premier League. That being said, it is still unclear how Google calculates the winning probability for each match. There is a suggestion that they use historical stats, others predict they use aggregated betting odds from various gambling websites, and so on. I even suspect they use Opta's LWP model to some extent. So yeah, it is still an unreliable metric and you should not use that as a basis to make any serious prediction at all imo.