"Time Exposures", a novelette by Wilson Tucker, first published in the 1971 anthology Universe 1 edited by Terry Carr. You might have read it in one of these compilations, among which is the 1979 anthology The 13 Crimes of Science Fiction (Isaac Asimov, Martin Harry Greenberg, and Charles G. Waugh, eds.), which can be borrowed from the Internet Archive (free but registration required).
This is a story about police investigating a crime scene with the aid of a camera that can photograph the recent past. However, the camera is not in a "floating ball", and nobody remarks on the fact that "if you’ve been murdered they cannot prevent that nor bring you back to life."
From the editorial blurb in Universe 1:
a quiet, matter-of-fact account of crime solving in the future, with a police camera that can photograph up to fourteen hours into the past.
From the story:
The camera itself was a heavy, unwieldy instrument and was lifted onto the tripod with a certain amount of hard grunting and a muttered curse because of a nipped finger. When it was solidly battened to the tripod, Talbot picked a film magazine out of the supply case and fixed it to the rear of the camera. A lens and the timing instrument was the last to be fitted into place. He looked to make sure the lens was clean.
Talbot focused on the front door, and reached into a pocket for his slide rule. He checked the time now and then calculated backward to obtain four exposures at nine o'clock, nine-five, nine-ten, and nine-fifteen, which should pretty well bracket the arrival of the janitor and toy shop employee. He cocked and tripped the timer, and then checked to make sure the nylon film was feeding properly after each exposure. The data for each exposure was jotted down in a notebook, making the later identification of the prints more certain.
The plainclothesman broke his stony silence. "I've never seen one of those things work before."
Talbot said easily: "I'm taking pictures from nine o'clock to nine-fifteen this morning; If I'm in luck I'll catch the janitor opening the door. If I'm not in luck I'll catch only a blurred movement—or nothing at all—and then I'll have to go back and make an exposure for each minute after nine until I find him. A blurred image of the moving door will pinpoint. him."
"Good pictures?" He seemed skeptical.
"At nine o'clock? Yes. There was sufficient light coming in that window at nine and not too much time has elapsed. Satisfactory conditions. Things get sticky when I try for night exposures with no more than one or two lamps lit; that simply isn't enough light. I wish everything would happen outdoors at noon on a bright day—and not more than an hour ago!"
The detective grunted and inspected the ticking camera. "I took some of your pictures into court once. Bank robbery case, last year. The pictures were bad and the judge threw them out and the case collapsed."
"I remember them," Talbot told him. "And I apologize for the poor job. Those prints were made right at the time limit; fourteen hours, perhaps a little more. The camera and the film are almost useless beyond ten or twelve hours—that is simply too much elapsed time. I use the very best film available but it can't find or make a decent image more than twelve hours in the past. Your bank prints were nothing more than grainy shadows; that's all I can get from twelve to fourteen hours."
