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All the King's Wine
Wine tends to only last about a week at most after opening, so the solution seems flawed as the king now has 999 bottles of spoiled wine and a bunch of dead servants.
Furthermore if nobody saw the thief poison a bottle it would be improbable to know that if a bottle was poisoned at all.
That's not to mention the method of injection, which for the sake of argument we will assume hypodermic needles have already been invented. With the amount of pressure it takes to insert a cork into a wine bottle I think it's safe to assume that the needle would have to be big enough to be durable so that it could even puncture the cork.
I would look for floating bits of cork inside the bottle, or assuming the wine had been collected over a period of time, examine the dust around the wine rack.context