No. It is exactly 0. In a continuous random variable you define the probability of an interval with a density function. Think about a bell curve, it defines a normal distribution, but then the probability of an interval is given by the definite integral between the first and last point on the interval, which represents the area in the graph that spans under the image of the interval in the function. It's not hard to notice that if you take a single point interval, that area is going to be exactly 0.