how was naruto chosen to be one the kyuubi would be sealed into?

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at first, i didn't understand why yondaime chose an infant to be the vessel of the kyuubi. i thought it was cruel but then i thought that maybe it was a requirement for the sealing jutsu that an infant should be used. after all, gaara was also an infant when the shukaku was sealed into him so maybe that's how the sealing jutsu works. but still, why naruto? is it because he's an orphan and nobody would object to it? was he just lying around nearby and he was the first infant that yondaime was able to lay his eyes on? i've heard of the theory that yondaime is naruto's father so that's why the kyuubi was sealed inside of him. but i don't see any sense in that. if he was yondaime's son, how come nobody in konoha seems to know about it? relatives of the hokages were treated like royalty. kabuto calls tsunade princess, and nobody punishes konohamaru no matter how naughty he gets and i'm sure it was also the same with asuma. it was totally the opposite with naruto. he was treated with contempt when he was growing up. it's possible that yondaime fathered naruto secretly so nobody knows about it. but i'm still not sure about that.