Real orthogonal group probability question

Let On be the set of all nxn, real, orthogonal matrices and let f be
the Haar probability measure
on On.

Fix x in R^n and e > 0 and let A(x,e) = {M in On: ||Mx|| < e} where
||.|| is the 2-norm.

What is f(A(x,e))?

Is there a closed-form expression? Upper/lower bounds? Can you gave
me a pointer to a gentle text for answering this question?

Thanks

.