Active probing began by measuring end-to-end path metrics, such as delay and loss, in a direct measurement process which did not require inference of internal network parameters. The field has since progressed to measuring network metrics, from link capacities to available bandwidth and cross traffic itself, which reach deeper and deeper into the network and require increasingly complex inversion methodologies. However, although active probing heuristics are based on queuing systems, to the best of our knowledge, a rigorous probabilistic treatment of probing methods has been lacking. As a result, important issues of system identifiability have been neglected: it is not known, even in principle, what can and cannot be measured in general, nor the true limitations of existing methods. We provide a blackprobabilistic treatment for the measurement of cross traffic in the 1-hop case. We first derive inversion formulae for the law of cross traffic and related processes, and explain their fundamental limits, using an intuitive geometric framework. We then use the resulting insight to design practical estimators for cross traffic, which we test in simulation and validate by using router traces. The estimators perform well, but have natural limitations, which are explained in detail.