In addition to former proposals, why not the famous two-volume work "Theory of Probability" by Bruno de Finette (In the Wiley classics series)
Quotation: "Probability do not exist"
A more modern book, with quite another take than the above, is "Bayesian Data Analysis", Third Edition by A Gelman, J B Carlin, H S Stern, D B Dunson, A Vehtari, and D B Rubin (CRC press). This a modern book with emphasis on data analysis and computation. I would say that for today (2017) this is the best starting point.