The Cloak

Curiouser and curiouser.

In the fourth book, chapter 25, Harry dropped the champion's egg and got stuck in the trick step. Moody tried to cover for him, but Snape knew.

"Potter!" Snape snarled, and he actually turned his head and stared right at the place where Harry was, as though he could suddenly see him. "That egg is Potter's egg. That piece of parchment belongs to Potter. I have seen it before, I recognize it! Potter is here! Potter, in his Invisibility Cloak!"

The first time through, Snape seemed to figure it out and guess that Harry was there. But after we learned about Legilimency, that section seems to show that Snape knew for a fact that Harry was there.

On the night of Dumbledore's "Murder," I assumed that Snape knew that Harry was present on the tower but, because the whole thing was a fraud, Snape pretended to not notice Harry.

Now I'm re-reading book 6, end of chapter 15, and I'm not so sure any more. During Slughorn's party, Snape and Draco step away for a private conversation and Harry evesdrops. When they leave, they walk right past him.

"Hardly daring to breathe, Harry remained crouched down as Snape emerged slowly from the classroom. His expresion unfathomable, he returned to the party. Harry remained on the floor, hidden beneath the cloak, his mind racing."

So, can Snape sense Harry's presence or not?

I don't think Snape can sense Harry's presence.
Concerning the instance in book 4: Snape knows that Harry has an invisibility cloak, knows he has the Maurader's Map, and knows Harry often sneaks around the castle at night. Then the egg fell. There were only four people that had one. Snape simply put two and two together.

But why would Snape expect Harry to hang around?
Without the trick step, he would have been long gone.

Egg, night strolls, cloak, map, trick step. And then there's the mystery of who was snooping in Snape's supply closet. That's a lot of two and two and two and two and two and two to put together so quickly.

I don't know, but Slytherin is the house of cunning. And that is a lot of two and two, but think about it where talking about Snape. Doesn't it all ways seem he knows what's going on.

That's exactly the point. That's a lot of information, which makes it easier to realize, not harder.

Good turn-around.
I didn't think of it that way.
Combined with that Slytherin cunning...