Suppose we want to say that event B is more likely than another A. What does that mean? A natural thing to say is that P(B)>P(A). But that doesn't fit our intuitions. For all measure zero sets then end up being equally likely. We can get a sharper comparison if we instead of starting with unconditional probabilities, we work with primitive conditional probabilities. A natural way that I've considered in the past is to say that A≤B if and only if P(A|A∪B)≤P(B|A∪B). This lets you compare tiny sets, like a single point to two points. But this approach has the intuitive disadvantage that then if we use uniform measure on [0,1], then [0,1]≤[0,1).
But there is a better way to generate a comparison from a conditional probability. Say that A≤B if and only if the two sets are identical or P(A−B|(A−B)∪(B−A))≤P(B−A|(A−B)∪(B−A)). It's not that hard (unless one is as sleepy as I am this morning) to show that this relation is reflexive, transitive and total—i.e., a weak order. Moreover, this weak order has the property that if A is a proper subset of B, then we're guaranteed to have strict inequality: A<B.
Update: A. Paul Pedersen informs me that De Finetti gives a definition equivalent to this on page 367 of the second volume of his probability book.