A 9000GH/s pool and a 9000GH/s solo miner will mine about the same number of blocks. Your hypothesis is basically nothing more than a guess, your rational doesn't make sense as they supposedly have similar hashrates, and your analogy is flawed.
Well your analogy is flawed. It's not like hunting for a missing person, where a pool has access to better resources than a solo miner. A hash is a hash, and after that, it's all numbers.
A better analogy is a a lottery that sells 100,000 tickets a day, and gets one winner a day. If you had a one person who bought 50,000 of those tickets, they would have the same "chance" as a collaboration of people who joined their funds together and bought the other 50,000 tickets, right? It's just statistics. Well if you take this lottery and keep it going every day for a month, eventually the winning tickets would be somewhat evenly split between the two parties.