A broken toenail does not necessarily equal a stubbed toe though.

If it's kills divided by deaths, then what's the score of someone who has never died?

Had the same thought.

It would be however many he/she has killed. A better way to think of it would be kills per life.

For example 10 kills, no deaths would be a score of 10. Average of 10 Kills per life.
And 10 kills, 1 death would be a score of 5. Average of 5 Kills per life.
10 kills, 2 deaths would be 3.33. Average of 3.33 kills for every life.

You see what I'm getting at?

Hmm wouldn't that mean a new player/game would have ∞ infinity on their ratio up until they die? Or NAN or the check would force assume 1 death so the division is still done correctly...

Same as the Game Center for Mac/iOS games. The first 5 or more are always exploited by hacks. I don't even look at them anymore.

Well, I did find this Pokemon video that demonstrates what happens when the game divides by zero:
https://www.youtube.com/watch?v=V6iUlyS8GMU

Some other games behave differently:
In SaGa 1 and 2 (on the Game Boy), the result of the division is 0.
In Final Fantasy 6 (possibly other SNES games?), the result is very high.

It just assumes you stubbed your toe and divides by 0.0005?

He can.

Plus the gamers who unlocked their achievements by hack. Steam does not really care about them except if they hack a VAC-enabled game. IMO, most hackers are kids.

Does the game has dense populated areas in which one could kill hundreds with a single AOE hit?

Depends on the weapon, and how densely they are. However the likelihood of a group being together closer than a grenade blast's lethal range is worth, it seems unlikely.

What does "VAC" stand for?

It is unfortunate that we cannot see more values on your screenshot, so that we can better look at patterns, but here are my thoughts on this matter.

First of all, the "reasonable" numbers seem to be rounded to the hundreds. That does not happen on #2, #3 and #4.
Second of all, it is expected that that scores follows a power curve. The abrupt change in scores breaks this curve.

I guess it means "Valves Anti Cheat" or some like that.
Hm, about the thing with multiple kills: I guess that one has to vaporize the population on a whole server with a nuclear weapon to archieve such a k/d rate. :-)) I`m not a multiplayer, but some of the games I play have such a k/d counter plus total kills counter and I wasn`t able to get beyond around 50,000 kills total even with over 100 hours of play. And I like to mention that those games are throwing hordes of enemies at you. So I guess it`s impossible to archieve millions of kills even in total, so the leader of this board must be some kind of a cheater!!!