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We had a new officer at our jail some time ago that put a clip into an AR, he then proceded to place the AR in an up-right position in the wall tower gun rack. The AR slipped out of his had fell to the floor striking the recoil pad. It was enough force to jar the bolt back, strip a live round from the mag (we don't keep a round in the chamber) on it's way back closeing. Then the free floating fireing pin had traveled upward strikeing the primer just hard enough to set off the round. The state internal investigators had locked him out of the jail for about 3 months saying that never could have happened and it would be a one in a million chance. Well they took the gun to test it by droping from the same height as it was said to have been droped from and it did the excatly the same thing for them. They tried it several more times but it never did it again. The officer was returned to work w/no questions asked. #1 rule with firearms is always keep the muzzle in a safe direction, as stated already.
One in a million chance? I would have to say that what you describe is almost impossible, one in ten million maybe. While a slam fire is possible, 99% of the time it's caused by the ammo rather than the rifle.
A standard precaution around PD's is to have a bucket of sand or something else to aim the weapon into when chambering a round, usually in their pistols, this is just good common horse sense, chambering a live round can be dangerous, so always pay attention to where the weapon is pointed when you chamber a live round in any weapon, not just AR's.