For starters, you have most of your facts wrong on those TV shows:
- Fox did not pick Arrested Development up for its latest season, it was shown exclusively on Netflix.
- Fox did not pick Prison Break back up after it canceled it, after the 4th season.
- Fox was not the first-run network for Freaks And Geeks; it was originally aired, then cancelled, by NBC. Neither network picked up the show for any episodes after the cancelled first season.
Having said that:
Fox cancels shows for the same reason all the other broadcast networks cancel shows: because not enough people watch the commercial breaks within the first three days of the first air-date of an episode. That's what advertisers pay for, and that's what networks care about.
Every other rating/number/ranking/etc is utterly meaningless, and exist largely to give networks things to brag about in an attempt to get more people to watch the commercials.
Shows are cancelled when those ratings are not high enough to justify continuing to pay for a show to stay on the air. Sometimes the ratings are so low that the amount of ad revenue a network could get wouldn't even cover the costs. Other times, the show's ratings are high enough individually, but low compared to the rest of the networks shows, making them less appealing to advertisers anyway. So the network will cancel their lowest rated shows even if they are technically still making a profit in hopes of finding better rated shows to replace them.
Bringing a show back is much more rare, and only happens if the network sees a way to make money from the show that they didn't before. Some examples of how this can happen are:
The production company may come back with a much-reduced production cost, making the economics work out better for the network. For example, if a network can squeeze 90ish episodes out of a show, they can sell it into the lucrative striped-syndication market (a fact that gets tons of otherwise undeserving shows a surprise 4th season). Usually, this happens before the cancellation becomes official, but not always.
The network may have noticed a much higher-than-expected return on DVD sales, something that tends to happen more with "highly IMDB ranked" shows, and decided that the DVD profit was worth the reduced first-run ad revenue. This is how Family Guy got un-canceled by FOX, for example.
The show may find an alternative outlet other than broadcast network TV. This happened to Arrested Development -- FOX did not pick the show back up, Netflix picked it up when FOX had no interest anymore. Since Netflix has far different economics than FOX, it can afford to air a different type of show.