Struggling here. The definition of Probability Distribution in my course text is not clear. The examples don't help much.

In Example 1 of a Probability Distribution Table they show female births with probabilities. That is to say, x = number of girls in two births where x is a random variable. So, the number of of girls can be 0, 1, or 2. Thus the probabilities are 0.25, 0.50 and 0.25 for each of the x values. I get this. No problem.

But then the next example asks, "When randomly selecting a jail inmate convicted of DWI the probability distribution for the number x of prior DWI sentences is as described in the following table:

x | P(x) |

0 | 0.512 |

1 | 0.301 |

2 | 0.132 |

3 | 0.055 |

But, this is a table of actual percentages where P(x) is really the percentage of values found/total selected. Isn't it? It seems to me the definition of a probability distribution in this case is contradictory. In the first case it was actual probabilities and in this case it's percentages. What am I missing here?