In their oral judgment, they stated "it was likely or more than likely" Mr Eveleigh had been driving at 124km/h. Mr Eveleigh said he was doing 108km/h.
Judge Peter Hobbs said that if Mr Eveleigh had appealed the conviction on the grounds police couldn't prove the speed he was travelling at, he would have lost the appeal.
"I am satisfied I have not been convinced that there is a legal requirement for a police officer to show a driver the speed recorded."
But a miscarriage of justice had occurred because the Justices of the Peace stated it was "likely or more than likely" he had driven at excess speed, not that they were sure, he said.
They weren't 100 per cent convinced of his guilt when they determined he was guilty, he said.
"They must be satisfied beyond reasonable doubt. That mistaken standard of proof does seem to me to be an error affecting the outcome of trial.
"It's not sufficient to think it is likely or more than likely. They must be sure. I am satisfied there has been a miscarriage of justice in this case."
Judge Hobbs granted the appeal, issuing a new infringement after Mr Eveleigh confirmed he was speeding at 108km/h at the time. His infringement fee is $30.
Outside court, Mr Eveleigh told the Times-Age he was stoked with the win.
"It should never have gone this far."
With a police officer following him, he would have been stupid to drive at such a high speed, he said.
"I knew he was behind me. It just didn't add up. I admitted to doing 108km ... I thought there was a speed tolerance of 10km."
