You could have such a fantastic, noir-y beginning if you spent just a short paragraph describing the murder scene--the blood, the position of the body, the surroundings. You do this a little later on, but you could really have a fantastic, visceral moment right out of the gate, as well as strengthen your characterization of Pro as a keen-eyed detective and give your reader a quicker sense of your world-building with one opening paragraph.
On p3, when he's arguing about the assistant, I think your aside ("Even if I did have time, I wouldn't want to" etc) is unnecessary--you convey that sentiment with his reaction before this--and spelling it out like that also makes him seem like more of a jerk than I think you're going for. Brash, yes, jerk, no. Or, at least, that's the sense I got from the rest of the chapter.
On p7, I had to re-read the transition between his barber and getting back out on the street a few times to figure out what had happened. It's a little brief and confusing, at least for me. I don't know if a paragraph break would help or another sentence, or if it's too minor an issue to stress over. You might also consider saving that for chapter 2 and tightening up the first chapter a little--the barber doesn't seem like he will be a particularly vital character, so he doesn't have to be introduced so early. I can see why you included this here--it gives more nuance about the expectations placed upon him by the people he knows and his reputation throughout his city--but you might consider scooting it a little later on.
On p7-8, his reaction to the guy seems a little at odds with the hard-boiled detective persona we saw earlier. A softer side of him would provide a more complex character, but it seems a little confusing here and at this speed. You could either make him a little more gruff with the guy--as in, still helpful, but a little less immediately so--or put this nuance a little farther in, when we've gotten a chance to know him better.
Also, more general, probably stupid question: are the Dhe like rats? I assumed "Dhe" was an abbreviation for the priests until right up at the end, when I couldn't figure out why a person would be crawling up the guy's leg. So, do the priests worship the rats? Do they just happen to take their names from the same etymological source? There might have been some explanation in the prologue, which I didn't read, but it was confusing for me.