The way I look at this is.
Let's suppose there are two mafia remaining, Falcon is obviously one of those. The other HAS to be either j0 or trangent, so in the worst case we have a 50% chance of finding it, even more if we catch a slip up.
On the other hand, the SK is tricker, it could be me (it isn't, but let's go with that), it could be KF, or it could even be j0 or trangent. Picking any of those gives us a 25% chance of finding the SK
But let's suppose axum wasn't lying and there are only three mafia. Then the SK is either trangent or j0, without a doubt, because there's no way both would be lying
Therefore, in both cases, lynching either j0 or trangent is the way to go, because we KNOW one of those is lying, no matter how many mafia there are remaining. It's a matter of probabilities, and I'd rather have a 50% chance of getting someone NO MATTER WHAT IS THE SITUATION OF THE TOWN AND THE NUMBER OF MAFIAS, than a chance that fluctuates between 25% or 0% depending on the number of mafias there are out there, that's just based on a hunch that, on top of that, is wrong