  We are interested in belief revision involving conditional statements where
the antecedent is almost certainly false. To represent such problems, we use
Ordinal Conditional Functions that may take infinite values. We model belief
change in this context through simple arithmetical operations that allow us to
capture the intuition that certain antecedents can not be validated by any
number of observations. We frame our approach as a form of finite belief
improvement, and we propose a model of conditional belief revision in which
only the "right" hypothetical levels of implausibility are revised.
