  The definition of conditional probability in case of continuous distributions
was an important step in the development of mathematical theory of
probabilities. How can we define this notion in algorithmic probability theory?
In this survey we discuss the developments in this direction trying to explain
what are the difficulties and what can be done to avoid them. Almost all the
results discussed in this paper have been published (and we provide the
references), but we tried to put them into perspective and to explain the
proofs in a more intuitive way. We assume that the reader is familiar with
basic notions of measure theory and algorithmic randomness.
