I have a question about how this process is supposed to work. What is the definition of a tie? Does that mean all five interviewers agree, three interviewers agree, or two agree? If two agree on the highest score, are both those scores thrown out? If three agree on the lowest score, are all three thrown out. Because I don't understand how the process is supposed to work, I can't even begin to analyze this.
Here is how I would analyze the much simpler problem of a three-way tie among three interviewers without the complications of discarding two out of five results.
First, I would not make HOI's arbitrary and highly implausible assumption that the scores are completely uncorrelated. Instead, I would make the much more plausible qualitative assumption that the scores are highly correlated. THEN I would make my own arbitrary quantitative assumption about what highly correlated means numerically in this specific case. I shall assume that it means that the difference between high and low scores will not exceed 10, but within this range scores are uncorrelated. (On a scale of 85, this is a relatively high spread.) Why do I assume that the scores will cluster. Because three interviewers are interviewing the SAME candidate; presumably, the qualities of the candidate affect the scores in a related way. It is easy to change this quantitative assumption so if you don't like it you can change it.
Say the low score is x and x < 76. Then there is a 1/11 chance that another interviewer will give the same score, but the chance that both the other interviewers will give the same score is (1/11) * (1/11) = 1/121. In other words, the probability of a three way tie is a bit under 1%.
What happens if we decide after looking at the results of many interviews that my guess at clustering was too broad and a better estimate is a difference of 5 between high and low scores. Then the probability of a three-way tie is
(1/6)(1/6) = 1/36, which is under 3%. So our analysis is not very sensitive to the quantitative assumption about spread.
Notice that my estimated probability of a tie is much higher than HOI's estimate. This is because he is assuming no tendency to clustering, and I am assuming a strong tendency to clustering. Different assumptions lead to different conclusions. But also notice that both assumptions estimate a probability of an exact tie as being relatively low.