Do all observations arise from probability distributions? Below is the quote from Karl Pearson in the book:  “The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century” by David Salsburg:

Over a hundred years ago, Karl Pearson proposed that all observations arise from probability distributions and that the purpose of science is to estimate the parameters of those distributions. Before that, the world of science believed that the universe followed laws, like Newton’s laws of motion, and that any apparent variations in what was observed were due to errors. Gradually, Pearson’s view has become the predominant one.

My question is on the use of the word observation. Does the above quote imply that any data we collect or observe in nature/physics/experiments arise from probability distribution? How about deterministic process, which surely in not probabilistic? Any expansion of the above quote for lay person would be very helpful.

A distribution can be thought of as a data generating function.
When we do inferential statistics, we collect a sample of observations, and then we try to use that sample to figure out the unknown distribution that generated that data.
The reason we want to know the distribution is because we might want to use a model to predict future observations. If we can figure out a good approximation to the true distribution then we can be sure that the future predictions will approximately follow the distribution and we will have a good idea of how accurate our predictions will be.
The distribution doesn't have to be probabilistic. It will still generate data that you can observe, even if the distribution is completely deterministic.
