As Tolkien says in The Silmarillion: Of the Rings of Power and the Third Age:
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Therefore the Three remained unsullied, for they were forged by Celebrimbor alone, and the hand of Sauron had never touched them; yet they also were subject to the One.
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Sauron made the One Ring to rule all of the others, not just those that he personally had a role in making, as is made clear in the above. In fact, the holders of the Three Rings knew instantly that they were in danger of being controlled as soon as Sauron put the One Ring on, so the connection there was quite clear....