In Trials of the Luremaster,
SPOILERS (maybe)
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You go up the East stairs, I think, look in one of the towers: the lower one, and you fight three poeple. one of them summons a genie. I think that dropped the bottle, or one of the humanoids did. What exactly does it do? At the moment, it is just empty.

The bottle is empty because that's where the genie came from. AFAIK, the bottle is of no further use and can be disgarded.

Does anyone know if you can prevent the guy holding the bottle from using it? or if it is possible to pickpocket the bottle from the guy?

I have not had the opportunity to test this but I think if you can get the bottle you will be able to summon the genie.

I have heard - but not tried - that if you're fast enough and kill the mage before he can summon the genie - you'll get a 'full' bottle.