How to approach rigorous probability theory from an economics background?
If you want a good book with emphasis on rigorous then An Introduction to Probability: Theory and Application, by William Feller is good source.
The book starts completely from the first principles and covers also a lot of applications in statistics. Arguably the book is more suited to graduate as it has a steep curve - the content difficulty increases rapidly, but I think that it can be suitable even at Msc level - especially if you are doing more research oriented Msc.
If you are would be interested in something more focused on econometrics then a primer in econometric theory by John Stachurski is good source although it does not cover probability so broadly as the above source.