<p>We study some <i>F</i>(<i>S</i>)-topology on the Borel probabilities supported on a topological space in this paper. Different types of vague and setwise topology are compared under certain assumptions on the space. We give explicit conditions for the two types of vague topology and the two types of setwise topology to be separable or metrizable on the probability measures. A necessary and sufficient condition for families of probabilities to be setwisely relatively compact is given in case the space is a compact metric space. These results and new types of topology are expected to provide more delicate tools in their applications to some stochastic processes.</p>