Given a dataset found by measurement $\{(x_1, y_1), (x_2, y_2),...\}$, what is $P(x_0| y_0)$?

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Assuming that a set of points $\{{(x_1, y_1), (x_2, y_2),...}\}$ has been found by measurement, what is the probability that, if $y_0$ has been measured, an arbitrary $x_0$ will be measured?

Would this probability be equivalent if $x_0$ was measured first instead?