No one knows what happens at a conditional baptism. One of two things may happen. If you were previously validly baptised nothing happens. If you have never been validly baptised before you will be baptised.
If the conditional baptism baptises you then you are freed from all your sins. However, because you cannot know what happened you need to go to confession: you don’t know if your sins were washed away or not.
In confession you should tell the priest that you are making a confession following a conditional baptism.