[mhneu]

If you're working through Spivek and Apostol, get Feller v1 and v2. Same level of rigor and emphasis on intuition. (If you're having fun after that, pick up Gallager's book on stochastic processes. Similar approaches, intuition, and focus on discrete probability to skip the metric theory complications of continuous dists.)

Another very good book is Bertsekas and Tsitsiklas, Introduction to Probability. This book will also give you some intuition.

I've heard Grimmitt recommended but I think B&T is better.

You could also start with Papoulis (a stochastic processes classic book, but it does the intro probability too.)

[abstrakraft]

In my experience, those who grew up with Papoulis, 2nd edition loved it. I grew up with Papoulis, 3rd edition, and find the layout and typesetting to be among the worst of any book I've ever read, bad enough to significantly affect usability and ability to quickly find things.

[mhneu]

Yeah, I personally don't love Papoulis. But it has been regarded as the standard stochastic processes text.