What is the meaning of “probability distribution of p(x)” of something uncountable?

Question

I'm studying VAE and new to both of the neural network and the statistic.

After some researches, I could understand the rough concept of VAE.
But what makes me confused is, the meaning of probability distribution p(x) itself.
When the x is an image data, what is the meaning of "probability distribution of the image"? and what is "probability distribution of the latent space"?

When I learned the probability distribution in school, x in p(x) was always something numerable(the value of dice, the number of apples, ..), and so I could get some value like p(x=1).
But I couldn't understand the meaning of p('image data'), p('latent space').
Although many websites explains the concept and logical flow of VAE magnificently, I'm stuck by the lack of my knowledge.

Anyone help me?