I have been asked this a bit lately so thought I would try and answer this question. The first thing you have to remember is that Space is big and mostly empty.
The asteroid belt is a doughnut-shaped ring which lies between the orbits of Mars and Jupiter.It is where most of the asteroids in our Solar System are found. They also orbit the Sun. It mist likely contains millions of asteroids.
Asteroids are rocky-metallic objects which range in size from about the size of pebbles to ~1,000 km across. Although they orbit the Sun, they are too small to be considered planets. Asteroids are thought to be leftover material from the formation of our Solar System. The largest asteroid is called Ceres. It is about one-quarter the size of our moon. It is a dwarf planet.
About half the mass of the belt is contained in the four largest asteroids: Ceres, Vesta, Pallas, and Hygiea. The total mass of the asteroid belt is approximately 3% that of the Moon.
Although most asteroids are found in the Asteroid Belt, astronomers have also identified a group of asteroids whose orbits cross Earth’s orbit. These are known as Near Earth Asteroids. Several hundred thousand asteroids are known to exist in our Solar System, and many are yet to be discovered. Most of the undiscovered asteroids are the smaller ones (less than 100 km across) which are more difficult to detect. It is estimated that there are over a million of these smaller asteroids.
NASA estimates the natural collision rate between two asteroids in the asteroid belt to be once every ten million years. Therefore, assuming a space probe moves at speeds comparable to an asteroid and is around the size of an asteroid, a space probe would not hit an asteroid in the main asteroid belt for ten million years, even if flying around blindly. Space is so big and so empty of rocks on average that unless a space probe intentionally aims towards an asteroid or a planet, it will miss.