The probability by which Bloom filters preserves the order relation given a similarity measure on sets A Bloom filter is a data structure for probabilistic set-membership. When adding an item to the set, $k$ bits (whose indices are determined by $k$ different hash functions) are set to 1. To check if an item is a member of the set, those $k$ bits are checked to be equal to 1. Deletions are no supported and there is a probability of false positives. 

Bloom filters are usually used make digests of big sets. In our case they are used to represent a set of items a certain user are interested in. Our clustering algorithm uses the similarity between the sets of two users (Cosine Similarity usually). However for the cryptographic version, we use the similarity between the corresponding Bloom filters of the sets instead.


  What I am seeking as whether there is
  any references regarding the
  conditional probability that the
  similarity between two Bloom filters
  will tell us something about the
  similarity between the corresponding
  sets, and to which degree Bloom
  filters preserve the order relation on
  Cosine Similarity (or other similarity
  measures).


I have been doing some work on that, and it gets pretty deep, lots of combinatorics and multi-set coefficients. I've posted a related question here. I tried to search for papers studying these properties as well and I did not manage to find something of much use.
This is not a direct answer to your question,  but it's related. The probability you want is precisely what is provided by min-wise hashing schemes. In particular, a min-wise hash takes a set and produces a single element, with the property that the probability of the two elements being identical is precisely the Jaccard similarity between the sets (intersection/union).