Good one Trainer!!
Usually knife "fights" start out as stabbings or knife assaults. There really isn't much lead in time, or like the movies where you have the big build up and the music swells and then the duel in slow motion. It's generally pretty quick. I have been fortunate, all my encounters with someone armed with an edged weapon they were never able to get it out. It was generally buried in their pocket, and at the beginning of the altercation they tried to go for it and I was able to smother their arm, or get them on the ground and gain control of them before they could get it out.
I had a shoplifter once who was stealing the reels off fishing rods and stuffing them down the front of his pants. When I caught him, he took off and tried to run away, but triped over his own feet (he was wearing cowboy boots) and I piled on top of him. He started trying to fish around in his pocket and I grabbed his arm. By then the other guys I worked with got there and we got him pinned. Once the police arrived, we found that he had a box cutter in each pocket. Even though he had 4 knives he couldn't access any of them quick enough, lucky for me.
I guess that is the long way of saying that they, like most altercations happen within a few seconds.