Roughly speaking, Inter, Milan, Juventus, Napoli will take 4 tickets
Why did you include Napoli in the team that qualified for the Champions League? Inter, AC Milan and Juventus are right because they have already locked tickets to the UCL next season. But Napoli is the team ranked 10th in the current standings. The teams in the top 5 have now confirmed their tickets to the UCL because their number of points can no longer be caught by other teams.
and Lazio, Atalanta, Bologna, Roma will apply for the remaining one with equal chances - so the chances on paper are 25%.
If you look at the current points, it seems like the teams in the top 5 have already locked tickets to the UCL next season. Ranked 5th is Atalanta and when it comes to chances, Atalanta has 66 points with 2 games remaining where As Roma has 63 points with 1 game remaining. Even in a situation where As Roma wins and Atalanta loses two matches, Atalanta will still qualify for the UCL because they have an aggregate goal advantage over As Roma.