January 26, 2017 11:28 AM

On Thursday, lawyers for Jeffrey MacDonald — the former Green Beret surgeon convicted of the 1970 murders of his wife and two daughters — argued his innocence before an appeals court.

The hearing took place before the 4th Circuit Court of Appeals in Richmond, Virginia and was over by 10 a.m. A decision could take months.

One of MacDonald’s attorneys said he was pleased with how the hearing went.

“The judges carefully listened to both sides,” Hart Miles tells PEOPLE. “They asked probing questions and certainly have a lot of material to consider. We remain hopeful that Jeff will prevail on his appeal.”

Prosecutors declined to comment afterward.

Whatever the outcome is, experts say MacDonald has defied the odds just to get his appeal this far.

That’s because a series of U.S. Supreme Court decisions in the mid-1990s made it nearly impossible to undo a wrongful conviction, especially if new evidence is discovered after a defendant has already lost one appeal — a scenario that applies to MacDonald.

“Even for an inmate who has powerful new evidence of innocence, it is incredibly difficult to get even a hearing in front of a judge to even present the evidence,” says Brandon Garrett, a University of Virginia law professor and author of Convicting the Innocent, a book examining the cases of the first 250 people exonerated by DNA testing.

“It rarely happens,” Garrett tells PEOPLE. “We have this idea that the federal courts are a front line defense against injustice and rights violations, but today it is almost impossible for even a stone-cold innocent prisoner to even get a hearing.”

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Jonathan Kirshbaum, a Nevada federal public defender who blogs about criminal justice issues on the website In Defense of Habeas, agrees with Garrett.

“Even before [a convicted person] can file the motion, he must first get authorization from an appeals court to do it,”Kirshbaum says. “It can be a daunting obstacle to overcome.”

Kirshbaum adds, “The fact that MacDonald was able to get that authorization in the first instance demonstrates how extraordinary his showing of innocence is.”

MacDonald, now 73, was convicted in 1979 of the murders of his wife, Colette, 26, and daughters Kimberley, 5, and Kristen, 2. He has never stopped saying he’s innocent, but prosecutors are just as adamant that he is guilty.

MacDonald’s hearing Thursday is part of an “actual innocence” claim, a legal term that sets a high bar for exonerations.

The 4th Circuit Court of Appeals granted MacDonald’s appeal request last April. The court will be tasked with determining whether a lower court was correct in rejecting MacDonald’s appeal, given the new evidence MacDonald has put forth since his conviction.

Says Kirschbaum, “The federal courts have repeatedly decided that there is something to his innocence claims. This is highly unusual. It is exceedingly rare for a federal defendant to meet all of these statutory standards. It shows that he does indeed have compelling evidence of innocence.”

In order to prevail, MacDonald has to show that, in light of the newly discovered evidence, no “reasonable fact-finder,” looking at the “evidence as a whole,” would convict him, according to previous court decisions in the case.

Each side got 20 minutes to make its case before the judge. The sides have already filed lengthy briefs detailing their legal arguments.

Both Kirshbaum and Garrett say that while it’s difficult to predict what the 4th Circuit will do, they believe MacDonald has met the extremely high standard to get his case tossed.

“There is powerful new evidence of innocence, including the DNA testing,” says Garrett. “It is hard to imagine that a new jury would convict in light of this new evidence.”

Garrett adds that in today’s climate, appellate judges are increasingly aware of the prevalence of wrongful convictions and the importance of considering new evidence.

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Says Kirshbaum, “I think MacDonald has a real shot at winning on the actual innocence argument.”

According to Kirshbaum, MacDonald’s claims are consistent with his defense from the beginning of the case decades ago.

“The Fourth Circuit is a very reasonable court and has shown a repeated interest in this case. I expect that the court will take MacDonald’s arguments very seriously. It is extremely unusual for a petitioner to come forward with so much exonerating evidence,” he says.

US Attorney John Stuart Bruce declined to comment to PEOPLE on the specifics of the case, saying in a statement: “When cases are pending court proceedings, it is the practice of our office to litigate the case in court — through evidence and argument in hearings and in written filings with the court — rather than through the news media.”

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