I am referring to Prof Andrew Ng Coursera ML notes (Week 9). He says that to identify outliers we first model the training data and then fit a Gaussian distribution with probability density $ p(X; \mu $, $\sigma^2 $ ). He then suggests that we can classify a new example $x$ as an outlier if "probability": $ p(x) <\epsilon $, where $\epsilon $ is a hyperparameter.
However, it doesn't make sense to me that how is he using term density and probability interchangeably without even explicitly mentioning it. I find this puzzling because if we assume $X$ to be a continuous random variable then $p(X=x)=0$ $\forall x$. Please help me in understanding what is actually going on in this algorithm at a finer level.