Given a data point $x$ and a possibly multivariate normal distribution $N_1$ with known mean and variance-covariance matrix, it is trivial to compute the likelihood of the data point $x$ given the parameters. In case we have a second distribution $N_2$ and a corresponding second likelihood, we can compute the probabilities that data point $x$ is generated by $N_1$ or $N_2$ by normalizing the likelihoods.
I was wondering whether there is a way to compute a probability that a given data point $x$ is generated by a given distribution $N_1$ without having more than one distribution to compute the corresponding second likelihood. That is, can we quantify the probability that $x$ is generated by $N_1$ given only $x$ and $N_1$? I am not sure whether this is possible and if it is possible, how to normalize the likelihood of $x$ given the parameters of $N_1$.