how does a dna probe work in DNA fingerprinting?
You should look up VNTR. Take a look at the wiki page and it will tell you that VNTRs are Variable Number Tandem Repeats, the length of which varies between individuals, making these irreplaceable in DNA fingerprinting and such. 

The trick is, all individuals will have it, but the pattern will be different, so you probe such regions which are formed as a stretch of k-mers. And you already know that they will be complementary, because we all carry them.