How are ETH 2.0 gas fees distributed?

Currently in ETH 1.0, gas fees go to miners. How will this work in Eth 2.0?

Will protocol fees be split proportionally between validators? E.g. if you are staking 1% of total staked ETH, you get 1% of gas fee tips (because base fee is burned via EIP 1559) in addition to 1% of the ETH emission rate?