We consider the problem of state estimation of a discrete time process over a packet-dropping network. Previous work on Kalman filtering with intermittent observations is concerned with the asymptotic behavior of E[P-k], i.e., the expected value of the error covariance, for a given packet arrival rate. We consider a different performance metric, Pr[P-k <= M], i.e., the probability that P-k is bounded by a given. We consider two scenarios in the paper. In the first scenario, when the sensor sends its measurement data to the remote estimator via a packet-dropping network, we derive lower and upper bounds on Pr[P-k <= M]. In the second scenario, when the sensor preprocesses the measurement data and sends its local state estimate to the estimator, we show that the previously derived lower and upper bounds are equal to each other, hence we are able to provide a closed form expression for Pr[P-k <= M]. We also recover the results in the literature when using Pr[P-k <= M] as a metric for scalar systems. Examples are provided to illustrate the theory developed in the paper.