Edit distance based string similarity join is a fundamental operator in string databases. Increasingly, many applications in data cleaning, data integration, and scientific computing have to deal with fuzzy information in string attributes. Despite the intensive efforts devoted in processing (deterministic) string joins and managing probabilistic data respectively, modeling and processing probabilistic strings is still a largely unexplored territory. This work studies the string join problem in probabilistic string databases, using the expected edit distance (EED) as the similarity measure. We first discuss two probabilistic string models to capture the fuzziness in string values in real-world applications. The string-level model is complete, but may be expensive to represent and process. The character-level model has a much more succinct representation when uncertainty in strings only exists at certain positions. Since computing the EED between two probabilistic strings is prohibitively expensive, we have designed efficient and effective pruning techniques that can be easily implemented in existing relational database engines for both models. Extensive experiments on real data have demonstrated order-of-magnitude improvements of our approaches over the baseline.