Rare event probabilities play an important role in the understanding of the behavior of biochemical systems. Due to the intractability of the most natural Markov jump process representation of a system of interest, rare event probabilities are typically estimated using importance sampling. While the resulting algorithm is reasonably well developed, the problem of choosing a suitable importance density is far from straightforward. We therefore leverage recent developments on simulation of conditioned jump processes to propose an importance density that is simple to implement and requires no tuning. Our results demonstrate superior performance over some existing approaches.