How does one know which eigenvalue corresponds to which probability?

I recently started grad school, and it's been awhile since I did any quantum, and this concept has got me stumped. I will try to elucidate the questions with an example:

Say I have an system spanned by orthonormal basis |1>, |2>, |3> and an operator A as follows:

A = (a,0,0; 0,0,a; 0,a,0) and |psi> = x|1> + y|2> + z|3> (where x² + y² + z² = 1). I find my eigenvalues of A to be a,a,-a. How do I know which probability amplitude corresponds to which eigenvalue?

I hope this makes sense, and I'm sorry I'm unsure how to format a matrix on reddit.