The car is probably going to be used in the 24 Hours of LeMons race so cheap upgrades are what l am looking for, mainly suspension upgrades.
Not the Le Mans in France, but the LeMons that is in the U.S., a race with cars worth less than $500, so l can not spend more than about $200 in parts.

You will need some good fog lights and upgrade you head lights so they shine further at night go to an air ride system so you can adjust it while you are doing your practice laps do not know if the rules will let you use air if not you can go to some kind of adjustable shocks and rear sway bar.and get some new windshield wipers

A Ford probe at LeMans ? l do not think so !
OK, enough jokes. Get a cold air intake, low restriction exhaust (if they require exhaust). If not, cut everything off up to and including the cats. A good set of plugs and 9mm wires. Tires are big for traction. New brake pads for sure. Honestly, $500 does not leave you many options. Have fun !

I'd probably just lower it a little bit if anything, the Probe is suspension is about as good as it is gonna be if u have a budget. Could try ebay for some coilovers, otherwise lowering springs. Strut mounts from a '97+ Escort also bolt in & drop it a little over half an inch, fronts for sure, not sure about rears. Maybe check u sway bar endlinks & make sure they're all intact as they have a tendency not to be, could also get strut tower braces. If cost is an issue u can build ur own endlinks using some threaded rod, eye hooks & high grade bolts.
Otherwise put it into necessities like headlights & speed like a cold air intake. You're not gonna get anywhere with the exhaust (except maybe a test-pipe to replace the cat) so unless you're chopping it off do not bother, any decent full exhaust is gonna run u at least $500 used.
And then, of course, there is weight reduction. Strip the interior & anything else u do not need. l would not see that being that big of an issue in such a long race though.