Classic Mafia - Conclusion!

[A-Man]

I was actually waiting for your answer xD

lol, predictable me.

Is it that bad to decide using the a priori probability of having a mafia there at the start of the game?

It's not bad, it just that this alone shouldn't make Bamboori any more likely to be a mafia. The probability of the beginning of the game has broken down to what's current and shouldn't be used as an implication to anything. In one branch of physics, everything is considered to be probabilistic. You do measurements like that all the time and it's known that a particle's "wave function"(possible states) collapses (narrows down to a fact) when you apply a measurement to it. Once the facts have been established, new possibilities emerge and the probabilities should change to fit these facts.

Edit:
Alright, here is another way that explains how using probability in that way is invalid.
Suppose I say I've made another list on day one of players, but in mine, I made a subtle mistake with the order I wrote the names:
1. AmadisLFE
2. Apocalipsis
3. Ramond
4. CosmicSarasa
5. Darl
6. empirefantasy
7. Jernemies
8. LutiChris
9. mfc
10.Bamboori
11.Rhino.Freak
12.Simoneon
13.TheNave
14.T.O.R.N.A.D.O

I just swapped the positions of Ramond with Bamboori. I arrange slots like you did and set a probability there exists a mafia player in each. By this time, I could say that Ramond should be your suspect because he is in Bamboori's place in my list. Now empirefantasyand says that he's written the list with few mistakes, but it was Tornado that was in Bamboori's place this time. But Tornado has been proved to be a civilian, and therefore your calculation is invalid. Now Simon appears and claims that he's made 14!(factorial) lists, and that every name has appeared an equal number of times in Bamboori's place. All of these would negate letting everyone retain their own original no.of.mafias/no.of.players.left probability.

Edit2: lol, seeing my old posts just shows how much this community has influenced me as a person.

Edit: Supposing you're a civilian, everyone is 2/(9-1). 2 is the number of mafia still alive. 9 is the number of players alive.