I think that it's Enbi, because in Chapter 3, he didn't say very much, and, well, the fact that he said "So, we all have cards?" or something like that implies that "Enbi" was not the real deal, because his rank was 5, so he would have been a registered detective for a long time, so I don't see why he would ask a question like that. I know that it couldn't possibly be Inuzuka, since only an actual detective could be capable of telling Yui's life story to her just by looking at her (a "Sherlock scan", as someone in the comments put it in Chapter 3). And Amino seemed to know what was going on, and what he was talking about, but Enbi though, just the fact that he seemed a bit clueless makes me think that he was the detective who was killed beforehand.

Then again, I could just be overthinking things, and maybe I got it completely wrong. Only time can tell.