That's an interesting analysis but it assumes all the games are independent of each other. In practice, I dont think they are. If a team gets on a roll, then they can become more likely to win their subsequent games. What were the odds on us winning our last 14 in 2019? Prob <1% (especially as we had come off a dodgy Xmas). But as we got closer and closer to the end, I think the players felt it would happen - which mattered greatly when we were struggling to break down Burnley and Leicester - and went a goal down to Brighton on the last day.
That doesnt apply to fans - I was a total wreck during that run-in, especially in the last 2 months.
I agree with your point. If you win, say, 4 games, then it's a bit more likely to win the 5th game than if you consider it in isolation (though not much more likely, as the role of chance can't be eliminated).
But I have inflated the percentages so that such a tendency doesn’t change the probabilities significantly. For instance, I've given Arsenal a 60% chance to win at Spurs, whereas the bookies give them under 45%.
Our run of 14 wins in 18/19 was unlikely, that's why such runs in the big leagues are rare, especially in England, Italy and Spain. Our second half of 18/19 was the best in the history of the big leagues.
So, in terms of cold numbers, the chance that Arsenal or Liverpool will win all of their remaining games is under 20% (from today's perspective). Things may change if the opposition teams suffer many injuries or get red cards, etc.
In the corresponding thread for the 21/22 season, I wrote that both Liverpool and City were likely to drop points in the remaining games after the draw at the Etihad (2:2). And they did, Liverpool vs Spurs and us vs West Ham. It's utterly difficult to win the final 9-10 games when you are in Europe as well.
Personally, I think that it is likely that either Arsenal or Liverpool will drop points in at least two of the remaining 7 games. How likely is it that both of them drop pts in at least two games? I think the chance for it is bigger than the chance one of them to win all of their remaining games.
Such calculations are no substitute for reality, though. In reality, something can happen even if the chance is extremely small...As they say, it's difficult to predict, especially the future :)