I'm honestly not sure if you can log the probe requests/responses via syslog. And even if you could, it would require A LOT of network traffic even if you had just a handful of APs.
You could, as a test, enable debugging for everything and then parse the logs to see if the probe requests or responses are logged, but since that's almost a layer 1 thing, I would be suprised if we actually push that via syslog. Associations and such likely are at debug, and authentication for sure.