"Ik ben de oudste van de drie."
Translation:I am the oldest of the three.
My initial feeling was that both forms are possible with a slightly different meaning.
In the end it might just depend on which part of speech you assign to the different words/parts of the sentence.
For superlatives het should be used when not followed by the noun being compared. (I can't get my link to a source for this to work but this is what it says in Van Dale grammatica Nederlands including some examples similar to the one here...)
Oudste can also be a noun and as such is a de-word but then would the van de drie part still make sense?
I am sure there is still more to it and maybe Stalker2106's living/inanimate also comes into it somehow even though I am personally not yet convinced about this explanation.
After more reading, my explanation is wrong!!! The words that are "het" are the neuter words, whereas, the words with a gender, are "de" words!
i.e. : "de man eet het brood". the man is masculine, bread is neuter. or "de man en de vrouw en het kind". Man and woman are "de" words, while kind, neuter, is "het"