If, in the opinion of the authority board, a special assessment is invalid by reason of irregularities or informalities in the proceedings, or if any court or other tribunal of competent jurisdiction adjudges the assessment to be illegal, the authority board, whether the improvement has been made or not and whether any part of the assessment has been paid or not, may proceed from the last step at which the proceedings were legal and cause a new assessment to be made for the same purpose for which the former assessment was made. Proceedings on the reassessment and for the collection of the reassessment shall be conducted in the same manner as provided for the original assessment. If an assessment or any part of the assessment levied upon any premises is so set aside and has been paid and not refunded, the payment so made shall be applied upon the reassessment.