- Negligence or carelessness, such as is seen in auto accidents and slip-and-fall cases.
It is vital to bear in mind that the mere fact of injury "even serious injury" does not necessarily result in liability. Sometimes people are hurt and there is no recourse (other than to their own insurance, if applicable); liability exists when there is fault, and fault is generally based on intentional acts or negligence.
Any liability in the situation described would presumably be based on negligence, since it’s very unlikely that the business intentionally caused the ice to make people fall. Then the issue becomes whether the business was in fact negligent, which depends on the circumstances.
As noted above, negligence is carelessness. If the business did not know there was ice and had no reason to know of the ice, and/or if there was no time to act on the knowledge, then there would be no negligence.
For example, say that ice formed overnight, and someone slipped and fell first thing in the morning, before staff or management had any chance to do anything about the ice - or possibly even to know it existed. In that case, there would be no fault. Similarly, there would be no fault if they knew there was ice and had taken reasonable steps, such as roping off the ice-covered area. If they took reasonable steps—what any reasonable person would do—and someone was still injured, they likely would not be negligent or liable. If ice were reportee and an employee promptly headed out to clean it up, but someone fell before the employee got there, the business might not be liable.
On the other hand, if someone had reported slick conditions and the business did nothing, that might make them liable. If a manager or supervisor saw the ice and ignored it, that would tend to create liability, as would not checking to see if a parking lot was safe after an obvious ice storm.
So in answer to the question—it depends. Specifically, it depends upon whether the business was acting as, and was as careful as, a reasonable person.