Since WW2 came up, 100 billion bullets is a reasonable estimate for how many small arms rounds were fired during the war. If something was literally a one in a billion chance, you’d expect to see it about once every two weeks to a month (depending on what you use as a start date).
Rifle bullets are much higher velocity than pistol bullets, it’s not surprising that a rifle round would do much more damage.
Maybe it did happen that often. In the chaos of combat, a soldier might not know it had really happened, and might subsequently fire his own gun, making it impossible to ever really know. And maybe there were a handful who were aware that it had happened to them, and it became just one of those strange-but-true war stories that they took home with them (if they went home alive). I wouldn’t necessarily expect it to be something that was terribly well documented.
It’s probably far lower than that. If I remember correctly, police hit their target in a real world fight about 50% of the time. I assume that “hit” includes any part of the target’s body, not just center mass. If you figure the area of the silhouette of the target and divide that by the area of the gun nozzle, and halve it, that should be about the probability you would expect for a confrontation where the target is facing forward with their weapon brandished.
I’m not sure what that is, but it’s probably more in the 10,000s range than the millions of trillions.
I was mostly putting the number out there so people would have a reference for how much ‘a billion bullets’ is. I would expect the chance for it to happen in the story to be something like the 1 in 1000 you estimated, but the chance on average over the course of WW2 to be much less. A huge portion of rounds fired in wartime would come from suppressive fire (especially from machine guns), which isn’t even aimed at a target but is intended to force people to stay in cover.