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In quantum physics the position of an electron is defined by a wave function. This wave function or rather it's square modulus is the probability distribution of the position of the electron. In more simple terms, the electron doesn't have a precise position but rather a high probability to be somewhere.
One example of an electron being able to be billion miles away is the following: Think of a probability in the shape of a bell. Where the center of the bell has a value between 0 and 1 and to each side the function tends to 0. The likeliest region for the electron to be is the center of the bell, but since the function never takes the value 0, it is not impossible for the electron to be a billion miles away.
If you apply a force to the electron, like an electrical field, you will simply shift and modulate the probability distribution moving the maximum probability towards the positive side of the electrical field. But the electron being in the place you expect it to be is still nothing but a very likely event. The event of the electron being a billion miles away is still of probability not 0.