So, when we use the 代名詞 の, it goes like this:
美味しいのをください Please give me the tasty one
静かなのはあれ The quiet one is that one
But what happens with adjectives or nouns that take a の already?
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Such の is called 体言の代用 in school grammar, and it is usually taught that it can be replaced with (の)もの/(の)こと.
According to a dictionary:
A possible source of confusion is that の can be replaced with のもの or もの, and the grammar does not differentiate them. My guess is that のもの replaces の when preceded by a noun (the first case above) and もの when preceded by others. Not completely sure, though.
The answer to the question: because 最後 is a noun, the correct form is 最後の＝最後のもの.
Other examples: 二番目の = the second one / 僕の = mine / 人の = other people's (things) or someone else's (thing)