Amanda Knox was cleared of killing British student Meredith Kercher by an Italian court in October.

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NEW: Knox's family issues statement praising the "proclamation of her innocence"

Judge: Prosecutors didn't prove Knox and Raffaele Sollecito killed Meredith Kercher

The two were acquitted of murder in October after appealing an earlier conviction

Prosecutors will probably appeal the acquittal, one tells CNN

Rome CNN  — 

The jury that cleared American student Amanda Knox of murder did so for lack of evidence proving she was guilty, the judge in the case said in legal paperwork published Thursday.

“Even taken all together,” the prosecution’s evidence does not “prove in any way the guilt of Amanda Knox and Raffaele Sollecito for the crime of” killing British student Meredith Kercher, the judge wrote.

Prosecutors will probably appeal the acquittal, prosecutor Giuliano Mignini told CNN on Thursday.

Either side can appeal a conviction in Italy, but appeals cannot be filed before the judge publishes the jury’s reasoning for its verdict.

An appeal in the Knox case would be on narrow technical grounds only and would probably take a day or two. It is unlikely Knox would return to Italy from the United States for the appeal.

Knox and Sollecito were convicted of murder in 2009 but cleared on appeal in October.

Knox was 20 and Kercher was 21, studying at the university for foreign students in Perugia, Italy, when Kercher’s semi-naked body was found November 2007 in the house they shared. Her throat had been slashed.

Sollecito, 23 at the time, was Knox’s boyfriend, studying computer science at another university in Perugia.

The case gripped the attention of the public in the United States, Italy and Kercher’s native Britain, where the tabloid press portrayed the defendant as femme fatale “Foxy Knoxy.”

A third man, Ivorian drifter Rudy Guede, was convicted separately of the killing. Guede admitted having sexual relations with Kercher but denied killing her.

Judge Claudio Pratillo Hellman said in the paperwork published Thursday that it was not up to the jury to reconstruct what had happened.

“What matters in reaching the ruling is only the lack of proof of guilt of the two defendants,” he wrote.

The jury was apparently convinced by a determined defense effort to discredit DNA evidence that played a role in the 2009 conviction.

Knox’s attorney, Carlo Dalla Vedova, said he was “fully satisfied” with the judge’s report, known in Italian as a motivazione, or motivation.

“We’ve always said that there was no evidence, that the first court ruling was based on probabilities and not facts,” Dalla Vedova said. “The first ruling was a mistake, which has now been corrected, so we are very satisfied with it.”

Knox’s family issued a brief statement Thursday saying the paperwork affirms “that Amanda had absolutely nothing to do with the tragic and terrible murder of Meredith Kercher.”

“Amanda and we are satisfied with the motivations and take heart in the strength of the judge’s words and proclamation of her innocence,” the family said in the statement.

CNN’s Hada Messia reported from Rome. CNN’s Richard Allen Greene wrote the article in London.