Are the tires three years old from date of manufacture, or do you mean they've been on the bike for three years?
Now, this is odd... I know the Michelin Lithion tires I used to run were date coded the same as motor vehicle tires, but I'm danged if I can find a date code on my Conti GP4000s or DH's Bontrager Race Lites. Anyone know what's up with that?
Anyway, NO, it's not "usual." Three years is getting up there, but it really isn't too long in the life of a tire. But, if the tires had already been sitting around for a year or two before you bought them, they definitely could be starting to harden and/or dry rot. Check them very carefully for brittleness. That'll be easy to do on the one that blew. Have you noticed that the tread isn't as grippy as it used to be?