> This would make it twice as likely that the remaining miners will mine each new block, right?

Not immediately. The "difficulty" of each block adjusts every 2016 blocks, the algorithm takes the average time between blocks and changes the difficulty accordingly so that the expected time becomes 10 minutes.

If half the miners stop mining, it will take around a month to mine 2016 blocks to trigger the difficulty adjustment, and that's if none of those miners stop mining before the adjustment happens. If the price keeps dropping and miners keep stopping, it could be 2 or 3 months before the adjustment happens