Three young Muslims shot dead. One white self-proclaimed atheist charged with three murders.

To some, including the relatives of the slain — Deah Shaddy Barakat, Yusor Mohammad Abu-Salha, Razan Mohammad Abu-Salha — the answer couldn’t be more clear. This man — the hulking, bearded Craig Hicks — killed them because they were Muslim. To pin their deaths on a parking dispute with the man is to ignore irrefutable facts. He was white. He had made comments. They were Muslim. And now they’re dead. “I mean, who would kill somebody over a parking spot?” Abdel Kader Barakat, Deah’s cousin, told the News and Observer.

Just look at the way they were killed, the family said. This was a hate crime.

“It was execution style, a bullet in every head,” Mohammad Abu-Salha, father of the women, told the newspaper. “This was not a dispute over a parking space; this was a hate crime. This man had picked on my daughter and her husband a couple of times before, and he talked with them with his gun in his belt. And they were uncomfortable with him, but they did not know he would go this far.” He recalled a conversation with his daughter, who lived near Hicks. ” ‘Honest to god,’ she said, ‘He hates us for what we are and how we look,’ ” he said.

“My cousin, his wife and sister in law were murdered for being Muslim,” Haya Barakat wrote in a message retweeted nearly 6,000 times. “Someone tell me racism/hate crimes don’t exist.”

It’s far too early to say exactly what occurred or why. Police have revealed next to nothing about what they’ve found so far, and their laborious investigation is just beginning. Hicks has not yet pleaded to any crime, nor offered any public statement.

But even if everything the family and many outraged Muslims say is accurate, even if the alleged killer did indeed “hate” them for what they are, it’s probably not enough to prove a hate crime under either state or federal law. That’s the experience of prosecutors across the country. Aggrieved groups don’t like it, for they are often seeking public validation of a genuine sense of injustice.

“Community members are understandably unhappy when an apparently race-, gender- or religion-based crime against someone they perceive as one of their own isn’t prosecuted as a hate crime,” said an article in the American Bar Association’s ABA Journal. “But this isn’t necessarily because of prosecutorial bias: It may simply be a function of how difficult it is to prove such cases, experts say.”

“Hate Crimes: Hard to Prove, Rarely Prosecuted” was the title of the journal article. The reason: Prosecutors have to get into someone’s mind at the time a crime was committed and prove to a jury not that someone perhaps hated but that “hate” was the motive.

The definition of a “hate” crime in North Carolina law, which does not use the word “hate,” is clear enough: A crime was committed because of a victim’s race, religion or sexual orientation.

“For most crimes, [intent] is the primary component that the state must prove beyond a reasonable doubt,” wrote legal scholar Gregory Parks. “For hate crimes, however, the state must also prove (beyond a reasonable doubt) that the defendant sought out the victim because of some cognizable characteristic” — such as race.

“It is unlikely that a defendant in such a case will readily admit to any racial animus,” wrote Parks. “Even when the defendant purposely chose the victim because he was black, Jewish, or gay, a confession substantiating this fact is not likely to be forthcoming. Instead, such motivation is likely hidden from authorities.”

Even when someone has a track record of hate — or of bigotry — it doesn’t necessarily mean that the crime was in any way related to that bigotry. This is the quandary that prosecutors faced in 2013 in Duncan, Okla. Two black teens were accused of shooting to death one white Australian college student.

One of the implicated teens wrote on Twitter earlier that he didn’t like white people. In fact, he even used the word “hate.” “90% of white ppl are nasty. #HATE THEM,” he said. Then in July, he again tweeted after the George Zimmerman trial. “Ayeee I knocced out 5 woods since Zimmerman court!:) lol sh** ima keep sleepin sh**! #ayeeee,” he said, using the apparent racial epithet of “wood” to signify a white person.

But even with that — a clear representation of disdain — prosecutors didn’t file hate crime charges. “The evidence is insufficient to establish that race was the primary motive in the murder of Christopher Lane,” said county District Attorney Jason Hicks.

“It’s much easier to talk about something being a hate crime than it is to actually go to court and prove that beyond a reasonable doubt,” former U.S. attorney Robert McCampbell, of Oklahoma, said in 2013. McCampbell said that tweet, while offensive, was difficult to link to the crime itself. “That doesn’t tell you anything about the day of this particular crime,” he told Fox25. “You concentrate on the crime in front of you and you prove that crime, and there’s no need to take on that extra burden of proving it was racially motivated.”

Even when a defendant has, for example, hurled bigoted words during an altercation — which can be circumstantial evidence of motive — prosecutors may have to “pinpoint when the racist motive was formed,” wrote scholar James Morsch in the “Journal of Criminal Law and Criminology.”

“In any number of cases, racism could have played little if any role in the beginnings of an altercation but have been injected into an argument later when tempers flared.”

It’s yet to be seen if authorities will turn up anything as significant as those tweets in Hicks’s background or anti-Muslim epithets during, say, an argument with the slain young Muslims in Chapel Hill.

Correction: An earlier version of this story misspelled the name of scholar James Morsch.