There is no "making progress" towards a solution. Every attempt has as good of a chance of being the right solution as every other attempt. Think of it like rolling dice. If 2 people each roll a die until one of them rolls a 1, are all the previous rolls "wasted"? Has anyone's chances of rolling a 1 gotten better (or worse) just because a 1 has (or hasn't) been rolled yet?
I don't entirely agree with this. In the dice analogy it would be more accurate to say that once a "1" is rolled the person who rolled the "1" will no longer roll another "1" because "1" has been proven to not be the solution to the problem at hand. That is, he would reduce the number of faces on the dice before rolling again. I agree that each attempt has equal chance of being the right solution in that the chance of rolling a "1" was just as good as rolling a "6" and that on the successive roll the chance of rolling a "5" will be just as good as rolling a "6" but chance of rolling another "1" has now been made zero and the available pool of possible answers has been reduced. Since the pool of possible answers is finite and thus every attempt proven incorrect will not be reattemtped the next attempt does run a statistically higher chance of being the correct answer than the previous attempt.