An analogy for mining would be the following:

You are at a lottery booth. The lottery booth has 1,000 lottery tickets in a bowl (which are always mixed perfectly). There is only one ticket with a prize in the bowl. Every time somebody buys one lottery ticket, the booth owner prints a new ticket and adds it to the bowl, replacing a loser with a new losing ticket, and a winner with a winning ticket, so that there is always 1 winning ticket and 999 losing tickets in the bowl.

Whenever somebody buys a ticket, chances are 1 in 1,000 that he wins.

You might win with your first ticket, but you might win with your 10,000th.

As you already mentioned, every try at finding a new block has an equal chance of being the winning ticket. That means that there is no such thing as "progress towards the block". It either works or it doesn't.

So now, somebody found a block. If people keep mining on the old block, they would have to find two blocks in a row in order...