7408 AND-gate IC giving HIGH output without giving any input
The assumption that connecting nothing means logic 0 is wrong. That is not how LS series chips work, as they consider no connection as logic 1 input. Also, leaving inputs unconnected can be considered bad practice anyway, so they should not be left unconnected to begin with.
And, you are also not supposed to short the chip output to ground, it is also incorrect use of the logic chip and can damage it.
Chips will only provide valid outputs with valid inputs.