The data deluge is defined by increasing amounts of large data with increasing degree of uncertainty. In a recent response, probabilistic databases are receiving a great deal of interest from research and industry. One popular approach to probabilistic databases is to extend traditional relational database technology to handle uncertainty. In this approach probabilistic databases are probability distributions over a collection of possible worlds of relational databases. On the one hand, research has seen various efforts to extend query evaluation from relational to probabilistic databases. On the other hand, updates have not received much attention at all. In this paper we show that well-known syntactic normal form conditions capture probabilistic databases with desirable update behavior. Such behavior includes the absence of data redundancy, insertion, deletion, and modification anomalies. We further show that standard normalization procedures can be applied to standard representations of probabilistic databases to obtain database schemata that satisfy the normal form condition, and can thus be updated efficiently.