"Preponderance of evidence" is a burden of persuasion. Burden of persuasion is the standard by which a party has to convince the trier of fact that the facts being asserted are true. In criminal cases, the burden of persuasion is "beyond a reasonable doubt." In some other situations, such as civil commitment proceedings, a burden of persuasion called "clear and convincing" is used.
"Preponderance of evidence" is the lowest standard. It is just enough evidence to make it more likely than not, that the allegation is true. If the trier of fact can be convinced that there is a 51% chance that the allegation is true, it meets the burden. "Beyond a reasonable doubt" is the highest standard.
In your situation, the government is going to have to convince the judge that you violated your probation, and the judge is going to have to be 51% convinced that you did violate the terms of your probation.
You should hire a lawyer or speak to a public defender.