I have a set observations of the same distribution with an unknown parameter. My statistics textbook says for two instances of the parameters, called $\phi_1$ and $\phi_2$, $\phi_1$ is more plausible value to be the true parameter than $\phi_2$ if $p(X = x | \phi_1) > p(X = x | \phi_2)$. I have no trouble to interpret the comparison of two probabilities of a random variable, for example p(X = a) < p(X = b) because I can rely on counting on the sample space of X to make sense the comparison. From my point of view conditional probability of different conditions are computed from different (sub) sample spaces so relying on counting to interpret does not work. How do you justify the comparison of the two conditional probabilities?