We report on a probabilistic weighting approach to indexing the scanned images of very short documents. This fully automatic process copes with short and very noisy texts (67% word accuracy) derived from the images by Optical Character Recognition(OCR). The probabilistic term weighting approach is based on a theoretical proof explaining how the retrieval effectiveness is affected by recognition errors. We have evaluated our probabilistic weighting approach on a sample of index cards from an alphabetic library catalogue where, on the average, a card contains only 23 terms. We have demonstrated over 30% improvement in retrieval effectiveness over a conventional weighted retrieval method where the recognition errors are not taken into account, We also show how we can take advantage of the ordering information of the alphabetic library catalogue.