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Suppose we are looking at an ordinal variable with $4$ categories. So there are three threshold coefficients $b_1, \dots b_3$ and one probit slope $b_4$. What is the interpretation of the following expressions: $$\frac{b_{1}}{b_{4}^{2}}, \frac{b_{2}}{b_{4}^{2}}, \frac{b_{3}}{b_{4}^2}, \frac{1}{b_{4}}$$

assuming a multivariate normal distribution?

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In what sense are you assuming a multivariate response distribution? Typically we think there is a univariate normal response distribution that has been categorized by replacing the value of the latent variable with an ordinal category based on where the value is relative to the thresholds. – gung Jan 4 at 20:16
Why are you looking at these expressions? The threshold divided by the square of the slope? Why would that be interesting? – Peter Flom Jan 4 at 23:23

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