Lack of information – average distribution of probability density

In many real problems we have to face up to information gaps. The paper presents the method of decreasing granulation of elementary events, which finds an average distribution of probability density, which represents infinite number of distributions. If we know the range of the unknown value and have qualitative knowledge about the general character of its distribution, then we can use this knowledge to surmount the information gap in a better way than the way proposed by the principle of indifference. According to the authors' knowledge the concept of the safe distribution is new and unknown in the literature. It is of fundamental importance for probability theory.