Well you can just read the reviews to see that the Durrett text isn't well regarded while others like Chung's are. And the criticism about a probability space not being a sample space is correct, but I think it's clear what Tao meant there, namely that the sample space would be a part of a probability space.
The Amazon UK reviews of Chung's book lead me to A Probability Path by Sidney Resnick which appears to be aimed at non-mathematicians. I have invested (speaking as a renegade physicist lacking a systematic exploration of measure theory).
