Before I respond, consider this: The mafia had already determined for themselves that Rich was the real detective. They also they knew well in advance of nightfall that he was their next hit.
As a side note, I think it's worthwhile for us to answer that question too.... "how could they have been sure it was Rich instead of Pir who was the real PR?"
That's actually quite obvious, now.
The mafia knew Piranha was lying the whole time --> because Piranha named an innocent as scum.
Pir's claim was wrong (they knew that); Rich's claim was right (they knew that too). The mafia knows who their teammates are.
The mafia, therefore, wasted NO time whatsoever trying to decide between Pir and Rich as the real detective. They knew it immediately, as it was happening.
So throughout the whole second day, all 5 of the mafia team - including Zaffy - pretended to be confused and unsure which role claim was the real deal.
Kash...don't you think the mafia knew Rich was the Det and Pir was lying because Pir is their teammate and they were just trying to get the Det to come out? Or do you think Pir is telling the truth now?