The chapter initially catches our attention with Gregson's letter relating the particulars of the case Holmes contemplates investigating. Gregson writes,
"There had been no robbery, nor is there any evidence as to how the man met his death. There are marks of blood in the room, but there is no wound upon his person."
The contradictions of the crime scene (blood but no wound, a man dead without cause or apparent motive) pique our interest and create both suspense (we want answers now) and mystery. Watson's views on the letter lend the matter a sense of urgency, increasing suspense. He believes the "terrible" matter is absolutely urgent: "'Surely there is not a moment to be lost,' I cried, 'shall I go and order you a cab?'"
Holmes's reluctance and apparent apathy only increase Watson's (and perhaps our) frustration. He feels that Holmes must hurry, and, filtered through his emotions, Holmes's "air of nonchalance which, under the circumstances, seemed to me to border upon affectation" as he "lounged up and down the pavement" begin to grate.
The suspense increases as Holmes doesn't explain his quiet exclamations while he studies the evidence that is incomprehensible to Watson (and, by extension, to the reader). We're kept in the dark while the detectives are left to emphasize the urgency and air of mystery surrounding the case. Lestrade says, "This case will make a stir, sir. It beats anything I have seen, and I am no chicken." The two agree that there is no clue—"none at all."
The suspense increases as it becomes apparent that Holmes has answers; he refuses, however, to reveal them, telling the detectives that "it would be robbing you of the credit of the case if I was to presume to help you."
Holmes's revelations at the end of the chapter regarding the appearance of the murderer don't really do much to resolve either the mystery or the suspense—now we're dying to know how he knows.