  The probability of there being sufficient inflation to solve the fine-tuning
associated with the horizon and flatness problems has recently been shown to be
exponentially small, within the context of classical general relativity. Here
this result is extended by considering loop quantum gravity effects, that are
significant at small scales. In addition to accounting for high-energy
departures from classicality, it is shown that, in contrast to the classical
case, the loop quantum cosmological probability measure is naturally finite, at
least in some well defined region. It is also shown that these loop quantum
gravity corrections can overcome the classical suppression of the probability
only for extremely unnatural choices of ambiguity parameters, implying that
single field, slow-roll inflation is exponentially unlikely.
