A conditional baptism is administered, I believe, when there may be doubt whether the candidate has previously been baptised.
This could be if a baby had been baptised by a lay person if there was a risk of death. Baptism can only be given once so if grandma or someone baptised the babe that would be valid.
Also, it can be given if an older person, for example, was converting to Catholicism and was unsure if they had been baptised.