If I was stopped in a store by a LP officer claiming I'm on video shown stealing on a previous day, what must the video show for a conviction?

Generally speaking to the limited facts presented:

First, you should hire a competent attorney, licensed to practice in your area and fully discuss the facts of the case with that attorney.

It appears that you are under the jurisdiction of a municipality (city or town), because the State (AL) does not have a crime of "petit larceny".  Generally, municipalities adopt the AL Criminal Code, but sometimes they do not or they change the names of the crimes.  We will assume that your apparent charge of "petit larceny" is what is defined as Theft of Property, Third Degree in the AL Criminal Code.  If so, the prosecutor must prove the following: 1.  That you knowingly obtained or exerted unauthorized control over the property of another person, 2. that you intended to deprive the owner of that property, and 3. that the property was valued at $500 or less.

This is a misdemeanor, so there is no jury.  The Judge decides the case at trial.  In order to prove that it was you in the video, the prosecutor has to convince the Judge that it was you.  The fact that the person in the video appears to have a jacket like yours is one factor the Judge should consider.  Your attorney should point out, if it is the case, that the jacket is the ONLY factor.  It just depends on what is actually in that video.  Your attorney should obtain a copy of it before trial, so that you and the attorney can make competent decisions about your case.

If the city or district court judge still finds you guilty (AL), you can appeal it to the Circuit Court for a trial de novo, or "new trial".  There, you will have a jury trial.