(CNN) After Aaron Hernandez was cleared of double murder Friday, prosecutors said victims' families took some solace knowing that Hernandez would not be set free. He was convicted two years ago of killing Odin Lloyd, so he is still serving a sentence of life without parole.

"If those appeals are exhausted, he will spend the rest of his natural life behind bars, so that does give the families -- and, frankly, our office -- some consolation," Suffolk County District Attorney Dan Conley said after Friday's verdict of not guilty.

However, Hernandez's attorneys have appealed for a new trial in that case. And Hernandez has shown a willingness to fight every charge against him.

So what are the chances he successfully appeals that prior conviction and, down the road, walks free?

Slim but not impossible, several legal experts told CNN.

"I don't see that happening," said Rosanna Cavallaro, a law professor at Suffolk University. "I don't think his fate changes because of this (verdict)."

Hernandez's appeal, which will take place at a later date, will try to combat his first-degree murder conviction for the June 2013 killing of Lloyd, who was dating the sister of Hernandez's fiancee.

How an appeal would work

Aaron Hernandez became emotional after the verdict was read on Friday.

In general, appeals cannot challenge what the jury found as fact, but they can challenge legal decisions by the court that influenced the case. For example, typical appealable issues include lack of sufficient evidence to convict, improper admission of evidence, jury misconduct or incorrect jury instructions.

If a higher court judge agrees with the defense's appeal, the judge could declare a mistrial and award Hernandez a new trial. Hernandez could then have a second chance to convince a jury he did not kill Lloyd, whose body was found in an industrial parking lot less than a mile from Hernandez's home.

"He's going to be hanging onto the hope and prayer that someday his other murder case will be overturned," said Philip A. Tracy Jr., a Boston-based attorney who has followed Hernandez's cases closely.

However, the chances of reversal are "not very high" in this type of murder case, according to Stephen J. Weymouth, a criminal defense lawyer in Boston.

"Not that many first-degree murder convictions get reversed," he said.

Even if defense attorneys identify a legal error, the higher court judge would have to certify that the error was harmful or material enough to have changed the case. Simple errors or minor issues could be declared harmless if they didn't affect the case significantly.

The Lloyd case was 'much stronger'

Unlike the most recent double murder case against Hernandez, the argument that Hernandez killed Lloyd in Bristol County was "much stronger," both Tracy and Weymouth said.

"There is not a great appealable issue," Tracy said.

Aaron Hernandez was sentenced to life in prison without parole for the June 2013 killing of Odin Lloyd.

Prosecutors in the Lloyd case tracked Hernandez's movements to the scene of the crime and showed surveillance video of Hernandez holding a gun, for example.

By comparison, the case against Hernandez in the killings of Safiro Furtado and Daniel de Abreu outside a Boston nightclub in July 2012 was largely based on the testimony of Alexander Bradley, a witness with a seedy past who received immunity to testify.

In addition, many legal issues and questions of admissible evidence in the Lloyd case were decided in favor of the defense, Cavallaro said.

For example, jurors in the Lloyd case were not allowed to hear that Hernandez had been indicted for the murders of Furtado and de Abreu. They also weren't allowed to hear testimony from Bradley alleging that Hernandez shot him in the face.

Those have proven to be smart legal decisions given that he was acquitted of those charges on Friday. If those decisions had gone the other way, Hernandez may have had grounds to appeal for a mistrial.

"I don't think there's any reason to be particularly optimistic about an appeal in Bristol County," Cavallaro said.

One appealable issue in Lloyd's case is whether any jurors improperly talked to an outside person about the case, but experts were skeptical of that as well.

"So that's the only thing they have, and I don't think it stands up very well," Tracy said.

Looking at it all, Tracy said there was just one clear path to Hernandez's freedom.

"His only way out of jail is a governor's pardon," he said.