Almost everyone thinks so, it would be strange if Manchester City did not get a ticket to the Champions League next season but so far their performance has not been stable this means that these 3 teams still have the same chance and yeah maybe luck can help one of them. The scenario would be different if Nottingham were to drop out of the top 4 which means Manchester City and Chelsea do not need to compete with each other while Newcastle deserve a ticket to the Europa League. We will see how the Premier League is at the end of the season at least after the remaining 9 games. The relegation zone is also interesting to wait because we saw West Ham close there.
With 9 games left I think City still have a chance to get 1 ticket to UCL next season. I think it would be very strange if they fail to qualify for UCL next season. The scenario I am thinking is Nottingham Forest play badly in a few games so Chelsea and City qualify for UCL next season. However I don't think Nottingham Forest will let that happen. They have been impressive this season and of course they will not waste the chance to qualify for UCL. They will try hard to get some wins and secure their position in the top four this season.