How to calculate perplexity of language model?
I believe he meant: you need to identify/predict a sequence of 4 consecutive things. First: an operator, then a sales person, then a technical support person, and finally one name out of 30,000 names. One and only one sequence is correct.

The probability of the correct sequence:

$$(1/4)*(1/4)*(1/4)*(1/120,000) = 0.0000001302083333$$

If you get the 4th root, that gives you the geometric mean (in some sense that's the average per step for four steps)

$$(0.0000001302083333)^.25 = 0.01899589214 ≈ (1/53)$$

So:

$$(1/53)*(1/53)*(1/53)*(1/53) ≈ (1/4)*(1/4)*(1/4)*(1/120,000)$$

It was however, not clear in the slides or the explanation.