The SUV was heading south on Highway 2 on the south side of the city when it went out of control Monday morning.
Insp. Gibson Glavin said it's believed the vehicle veered onto the shoulder of the road, over some rumble strips.
"It appears as if the vehicle took a sudden jerk away from those rumble strips, as if someone was trying to correct the vehicle's direction. And that caused the vehicle then to roll several times in the middle of the southbound lanes."
Glavin said three people were pronounced dead at the scene but could not provide details about them, including their ages.
A woman was airlifted to an Edmonton hospital with significant injuries and was in "very grave" condition, he added.
He said it's not yet known which person was driving.
The divided highway, a main link between Edmonton and Calgary, is one of the busiest in the province. But Glavin said no one else was injured as no other vehicles were near the SUV at the time of the crash.
He said debris from the mangled SUV littered the road and its southbound lanes were closed to traffic for about five hours.
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