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It's not "1-is-not-a-probability" so much as it is "the base rate of this is not 0"; there's also the chance that I was switched at birth (hospitals are much better at avoiding this now than they have been in the past). If my family signs up for 23andMe, then the probability will either shoot up towards 1 or drop down to negligible, but until then I'm going with the base rate.
Really during your life you haven't encountered much net evidence towards either direction shifting your probability assignment away from the base rate, e.g. how much you look like your parents, whether you share some uncommon medical condition with either of them, blood type, etc.?