Shaykh Abdul-Muhsin al-Abbaad was asked the following question:
We have with us in Russia some sweets that are made with alcohol, but these sweets do not intoxicate [a person] even if a lot was eaten. This is an issue that has made a lot of confusion for us, so we hope for clarification. Does this enter into the prohibition or not?
If a lot of [these sweets] do not intoxicate, then it does not affect. As long as it does not intoxicate, then it does not affect. Verily that which is prohibited is what intoxicates in a large amount, so a small amount is prohibited like a large amount.
[Sharh Tirmidhi no. 206]
Faisal Ibn Abdul Qaadir Ibn Hassan