Previous research applying kernel methods to natural language parsing have focussed on proposing kernels over parse trees, which are hand-crafted based on domain knowledge and computational considerations. In this paper we propose a method for defining kernels in terms of a probabilistic model of parsing. This model is then trained, so that the parameters of the probabilistic model reflect the generalizations in the training data. The method we propose then uses these trained parameters to define a kernel for reranking parse trees. .