Politkovskaya, who wrote books and articles that fiercely criticised Vladimir Putin, the then Russian president, was shot dead in her central Moscow apartment building in October three years ago.
Many of her colleagues have suggested her murder was linked to her investigative reporting of abuses committed by Russian troops as they battled separatists in the republic of Chechnya.
'The big question'
Speaking to Al Jazeera, Alexander Nekrassov, a Russia analyst and former adviser to the Kremlin, said: "The question mark [in the original trial], I suspect, for the supreme court, was that some of the witnesses were afraid to testify ... some of the information was suppressed.
"The question against the decision to order a retrial is that these are not the people who pulled the trigger, these are not the people who ordered the murder.
"So that is very strange, to see that the prosecutors are actually targeting these three. Why don't they go and search for the people who actually organised the whole thing and who paid for it?
"That is the big question that people have."
Neave Barker, Al Jazeera's correspondent in Moscow, said: "The case was heavily criticised, not only by friends and colleagues of the murdered journalist, but by political figures as well.
"They say that the case not only failed to bring the actual killer to justice, the person who pulled the trigger has never been found, nor has the person who ordered the killing.
"During the investigation itself, vital evidence reportedly went missing, including mobile and sim card information, computer disks and photographs and the footage of the assassin actually entering Politkovskaya's apartment."
Anna Stavitskaya, a lawyer for the Politkovskaya family, said they did not support the annulment of the verdicts.
"They were completely in agreement with the acquittal verdicts, we did not regret this and we think there is no foundation for their annulment," she told the RIA Novosti news agency.
The original trial, which lasted around three months, did not shed any significant light on the circumstances of the killing.
It also cleared a fourth man, Pavel Ryaguzov, a former agent of the FSB security service, who was accused of extortion in connection with the case.