Assuming that there is 4 scum total and one in the neighborhood –which is the best case for lynching in-neighborhood – it is indeed true that the prior chance to hit scum when lynching inside is slightly worse than that of hitting scum when lynching outside, from my PoV. There are 12 players left, 3 in the neighborhood, 9 outside, 8 of them aren't me. So outside it's 3/8 and inside it's 1/3 = 3/9, which is lower. The reason why I want to lynch inside anway is threefold
a) most people have been pushing for a lynch outside, which is a sign that scum is inside
b) I strongly townread EFHW and townread DatSwan which makes for excellent PoE.
c) This is the most important point: if we lynch scum in the neighborhood, we create 2 ICs. If we lynch scum outside the neighborhood, we create 0 ICs. Creating 2 ICs is super awesome. If scum targets them, great, they're not targeting PRs. If scum does not target them, great, we have 2 ICs.
The fact that we're in a tough spot should be an argument to do high risk play.