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You don't choose a target for Snaremaster Sprite's ability at the time it triggers. Rather, a second "reflexive" ability triggers when you pay {2} this way. You choose a target for that ability as it goes on the stack. Each player may respond to this triggered ability as normal.

You may target a creature that is already tapped with the reflexive triggered ability. If the target creature is already tapped as the ability resolves, you will still put a stun counter on it.