How do you properly break a 3-way tie, FAR 14.406-8 doesnt prescribe ways to break tie.
Three offers at exactly the same price is statistically improbable and you may want to refer this to the attorneys to insure that this does not involve price fixing.
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To answer your specific question, when there are more than 2 identical offers, you can take 2 long pieces of paper and one very short piece of paper, which are placed in an elevated hat. The papers are folded over so that they are the same size. The branch chief or attorney or other designated official (not the contracting officer or specialist) then draws a paper for a company- I suggest you go in alphabetical order. The short paper gets the contract. You can also do it with marbles or coins (make sure you have 3 of the same coin, but different dates, then specify in advance the date that wins).
Document in writing everything that happens before and after the selection and make sure you have several Government employees as witnesses.