That may not seem like a high probability, but consider that most mammals are estimated to carry 80-100,000 genes. This suggests that every individual born has a good chance of carrying one new mutation in some gene. Dominant mutations will be expressed and any that are deleterious will be eliminated almost immediately from the population. New recessive mutations remain hidden from selection until they reach a frequency where some homozygous individuals begin to appear. However, this does not prevent drift loss, which doesn't depend on phenotype.
Drift is a consequence of the random nature of genetic events.
For example, if you breed a brown bitch to a black dog carrying brown, you would expect the progeny to be black and brown, but probably wouldn't be too surprised if you got 7 blacks and 3 browns in a litter of 10. It works the same way for any gene that has two or more alleles. The one Bb dog may pass the B allele to none or all of his progeny, or to any number in between. If he has more than 5 black progeny, the frequency of black will go up providing all contribute equally to the next generation. In subsequent generations the frequency may drift even higher, or back down.