(My comment was generated by the spontaneous reaction and reflection of a native speaker rather than memory of any deliberately learned rule.) Wikipedia has this to say:

In English and some other languages, the use of such a word implies the definite article. For example, my car implies the car that belongs to me/is used by me; it is not correct to precede possessives with an article (* the my car) or other definite determiner such as a demonstrative (* this my car)

One should indeed think of " 's " in this context as the equivalent for nouns of what "my" is for the pronoun "I".