Nothing has changed between this and using mathematical chances and it think that the result can still chance but yeath since the upcoming week is not gonna be a hard week for manchester cit and in my opinion that if nothing will change. Liverpool is still leading the competition, but given the upcoming fixtures between Liverpool and Arsenal which are even more difficult compared to the what manchester city is gonna face and i strongly believe city can take advantage from this, I believe a miracle can occur for Manchester City in the future to see its competitors were bottling some matches. Having said that if Liverpool is currently favored by bookmakers to win the competitions but who knows if a miracle can happen like last season when arsenal bottled some matches, but there are still plenty of matches left for all of top clubs and the standing can changed based on the resut achieved in any weeks.

The first, second, and third positions can change at any time as long as the gap is not too large. I believe Arsenal should have a lower win probability based on who their next opponents will be. Manchester City has surpassed almost all of the strong clubs but yeah since it was not lucky enough and it's still at the third place now.
city now only has some mediocre clubs as upcoming fixtures which can be passed easily by the big like city and it will put the city in the safe zone, whereas Arsenal has not yet faced strong clubs. We consider other factors, such as club fixtures and I would rank Arsenal lower than Manchester City coz city has easier fixtures compared to the arsenal which will face chelsea, mu and many more.

Liverpool will remain in first place if they do not have as difficult a schedule as Arsenal. I believe the Reds will win the competition this season because they have a very strong club that can perform consistently in any match.