Wow, beaten to the narrow answer already.

BUT, getting on to the broader answer, you need to realize that 81/3,650,000 is the chances, specified ahead of time, of that particular match.

If you’re just noticing a particular coincidence after the fact, remember, there is also a chance the birthday would match with European numbering (day-month-year), or year-month-day, and a chance the four SSN digits are exactly the same as the four-digit year, and the chances of all the other ways a birthday could be somehow matched to four digits. So if you’re asking ‘what are the chances a birthday could match the last four digits of the person’s SSN?’ then the answer is really “Well, always, if you’re creative enough to find a particular way of matching them.”