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This material needs major reconsideration or deletion. It does carry the references. The principle of vacant places follows from Conditional Probability theory, which is based on Bayes Theorem. For a good background to bridge probabilities, and vacant places in particular, see

• Hugh Kelsey and Michael Glauert: Bridge Odds for Practical Players, ISBN  0-575-02799-1.
• H.G. Francis, A.F. Truscott and D.A. Francis (Eds.): Mathematical Tables The Official Encyclopedia of Bridge, 5th Edition, ISBN  0-943855-48-9.