Is it possible to get an ex back after no contact for three years ?
How to test whether she is still interested without letting her know ?

Why would you want her back? What is the back story to all of this

That is a LONG time to be broken up, and I wonder what has gone on in your life between now and then that makes you want her back? You haven't even talked to her or seen her in three years... something isn't right here. More info is needed.

Ask her!