Yes, it's probative. As it suggests the victim might previously have been involved in burglaries. Which would make the shooter's story that the victim was acting suspiciously, at least to some extent, more believable.
Just as it would make his claim of self-defense more believable if it happened to be that the victim had previously attacked other people.
Unless Zimmerman knew about it, it has no bearing on whether or not he had good reason to be suspicious of Martin. The only question that is at all relevant is whether Zimmerman was reasonable to be suspicious (although the only question that is really going to matter at trial is whether Zimmerman reasonably feared death or serious injury when he fired the shot). Things that Zimmerman did not know at the time are not helpful in answering that question.
This is the first time I have seen it suggested that there is any likelihood that Martin actually was about to commit a burglary. We know Martin was staying nearby and had walked to the store, and was returning home. Given that very plausible explanation of Martin's behavior prior to Zimmerman following him, how exactly does the screwdriver incident constitute a reasonable basis for concluding that it was even remotely likely that Martin was about to burglarize anyone's house?
Zimmerman was suspicious based on what he knew at the time, and what he observed. We have the benefit of knowledge Zimmerman didn't have, so this is not to judge Zimmerman. But which is more relevant, the screwdriver thing or the fact that Martin was staying in the neighborhood? If Zimmerman had known that Martin was staying in the neighborhood, then I don't think he would have found him suspicious, or at least not suspicious enough to follow him. Even if he had also known about the screwdriver thing at school. That is also my attitude, since I know both of those things. Do you disagree with that attitude? Do you think
I, who have this knowledge that Zimmerman did not have at the time, would be reasonable in thinking (now, in hindsight) that Martin was
actually up to no good because of the screwdriver thing? Because if not, then it is indeed irrelevant.
For the record, I am not saying this because I am of the opinion that Zimmerman racially profiled Martin. From the call, it seems that Zimmerman's suspicion was based on
(1) the fact that he knows the people who live in the neighborhood and didn't recognize Martin,
(2) that Martin was walking in the rain (which looks more suspicious in light of point (1), since Zimmerman believed that Martin did not live in the neighborhood),
(3) that Martin was walking in a way that I would describe as "sauntering." It is that way silly teenage boys who want to appear tough walk. I saw it all the time as a teacher, and personally would think nothing of it. But people who have never worked around kids that age tend to interpret it as "thuggish." And,
(4) the fact that there had been a series of burglaries recently.
Given the above, I do not think Zimmerman was unreasonable to be suspicious. Reason (3) is not a good reason, but the others are reasonable. And they were reasonable even if in fact Martin was doing nothing wrong. I don't think Zimmerman
acted wisely on his suspicion, but he had a legitimate basis for his initial suspicion. The screwdriver thing would only be relevant if there were some other reason to believe Martin
actually was up to no good that night. There is absolutely nothing to suggest that. I don't think even Zimmerman
now thinks that Martin actually was a burglar. I doubt he would have apologized to the family if he believed that. I think he thinks it was a tragic misunderstanding that led to a situation where he was in fear of his life and had to shoot in self defense.