Making sense of avuncular test results

I just received results for an avuncular DNA test that a young lady & I.  I may be her aunt (my brother's daughter).  My brother does not wish to provide a blood sample, so she & I did.   The company that we used stated that the probability of the 2 of us being related is 24.24%.  She & I share one or two alleles for:  TH01 (6), D18S51 (16), Penta E (13), D13S317 (8), D7S820 (8), CSF1PO (11), Penta D (12), vWA (16), TPOX (8 AND 11).  Now, call me an optimist, but I would think that 24.24% is pretty high & the liklihood of two unrelated people sharing these alleles pretty low.  However, I don't know a thing about genetics & I have no clue as to how common these particular alleles may be.  What are your thoughts?  I asked her mother last nite if she'd be willing to provide a blood sample, although I'm concerned that this may be a waste of time.  Help!