2a) Yes, because lottery tickets have a large number of smaller prizes, and there's a non-trivial chance I won one of those.

b) Aside from natural human disbelief, fairly high. The only alternative hypotheses that come to mind(assuming it's a reputable lottery and I'm sure I'm on the right site) are that they mis-posted the numbers, but there's no good reason to believe they'd have picked mine there, and their posting error rate can be estimated at perhaps 0.1%, so I'd be 99.9% confident if that's the only alternative. Some sort of smartass scam is possible, but really unlikely. (I'd double-check the dates, of course)

c) Ticket verification, again assuming it's a reputable lottery. Money in the bank if it's a fly-by-night operation.