In the years investigators spent scouring through what might have motivated Bryan Kohberger to murder four University of Idaho students, they found no sign that he had connected with his victims on social media. There was no evidence he had visited their home. There was nothing to suggest that he had ever met them.

It is even possible that he did not select the house as his target until just before he entered it around 4 a.m. one night in November 2022, the lead prosecutor in the case said in an interview on Thursday.

After Mr. Kohberger’s sentencing to life in prison for the crimes on Wednesday, and the end of a court-ordered prohibition on discussing the case, prosecutors and investigators have started dispelling the many rumors surrounding the case — theories and suspicions that have long served as the basis for erroneous news coverage and endless social media debates.

Bill Thompson, the lead prosecutor in Latah County, where the killings happened, said investigators had hunted extensively to establish a prior connection between Mr. Kohberger and the four students — something to suggest why they were targeted. But if there was a connection, it remains a mystery, he said. It is possible that Mr. Kohberger’s attack was one of opportunity, he said, with the victims chosen at random.

“We simply don’t know the answer to that,” Mr. Thompson said. “And human nature is, we would like to know the answer, an explanation for everything. We want everything to make sense. But what we’re dealing with doesn’t make sense in and of itself.”

Mr. Kohberger himself did not detail his motives during his brief statements in court.

Prosecutors said Mr. Kohberger drove to the victims’ home in the city of Moscow near the University of Idaho campus early on Nov. 13, 2022. They said he sneaked inside and fatally stabbed two women in one bedroom before fatally stabbing another woman and her boyfriend on another floor.