We know. (The situation should be something like the following: internal statements about the probabilities assigned to various statements get interpreted in nonstandard models, so the corresponding probabilities are nonstandard reals.) Nonstandard models are an essential component of the approach here: probability assignments are the same thing as probability distributions over models (only one of which is standard).
Regarding the epsilons and stuff: you guys might want to look in to hyperreal numbers.
We know. (The situation should be something like the following: internal statements about the probabilities assigned to various statements get interpreted in nonstandard models, so the corresponding probabilities are nonstandard reals.) Nonstandard models are an essential component of the approach here: probability assignments are the same thing as probability distributions over models (only one of which is standard).