How do probes fly through an asteroid belt?

How can they fly through one without hitting anything?

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Mr. Boxy

Almost every sci-fi show or movie involving space ships at one point has a scene in which the good guys, who are hopelessly outnumbered, fly into an asteroid field to escape their enemies. There are so many rocks flying around that large ships can't possibly enter, and even small ships require expert piloting to avoid a crash. The good guys survive while the bad guys have to fall back. Even Star Wars used this common trope:

However, real asteroid fields are far less dense. There is enough debris in the creatively-named Main Asteroid Belt between Mars and Jupiter that scientists think it may be the remains of a planet, but it is almost evenly distributed in orbit. This means there can be hundreds of thousands of miles between one asteroid and the next. Even then most of these asteroids are the size of pebbles, representing no real danger to a vehicle designed to withstand the debris in Earth's orbit.

So far nine probes have flown through the Main Belt, and none of them have had any damage due to asteroids.

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