The motion of passively convected particles in turbulent flows is studied experimentally in approximately homogeneous and isotropic turbulent flows, generated in water by two moving grids. The simultaneous trajectories of many small passively convected, neutrally buoyant, polystyrene particles are followed in time by a particle tracking technique. We estimate the probability distribution of the occupation times of such particles in spherical volumes with a given radius. A self-consistently moving particle defines the center of the reference sphere, with the occupation time being defined as the difference between entrance and exit times of surrounding particles convected through the sphere by the turbulent motions. Simple, and seemingly universal, scaling laws are obtained for the probability density of the occupation times in terms of the basic properties for the turbulent flow and the geometry. In the present formulation, the results of the analysis are relevant for understanding details in the feeding rate of micro-organisms in turbulent waters, for instance.