Not a nat bar nat, but a direct nat. Blood spotted egg to water. The kosher eggs are cooking in this blooded egg “soup”. Eggs are porous and directly absorb or emit their status. The pot would become forbidden, so too the water and also the other 2 eggs
To illustrate, suppose by mistake you cooked 2 chicken eggs with an eagle’s egg. The 2 chicken eggs are treif (midrabonan, because there is no 60:1), the water is treif, and the pot is treif.
If you are in agreement, explain the difference between the third egg being an eagle’s or being blood spotted?
(.I am asking based on opinions that todaay blood spotted eggs are forbidden – the question does not apply if they are mutter, but then there is no need for cooking three eggs at a time to do a bittul, right?)