Is formation of a black hole thermodynamically favourable? Isn't it like that the black hole is just swallowing suns and other parts of cosmos, and thus continuously absorbing matter. I know that it emits radiations also, which should be negligible in terms of the absorbed matter and thus energy. If the net internal energy of a black hole is just increasing and it's entropy being decreasing, then doesn't it's existence disfollow the laws of thermodynamics?
 A: Intuitively, it might seem that black holes have low entropy, but that is not correct. Their entropy is in fact gargantuan. For example, as mentioned in the Scholarpedia entry for the Bekenstein–Hawking entropy,

Note that a one-solar mass Schwarzschild black hole has an horizon area of the same order as the municipal area of Atlanta or Chicago. Its entropy is about $4\times 10^{77}$, which is about twenty orders of magnitude larger than the thermodynamic entropy of the sun.

(See, e.g., this post for
a bit on the entropy of the Sun).
Hence, black holes are actually quite favorable from a thermodynamic point of view, provided that there is a sufficiently high density so that the black hole can form. For example, Gibbons and Perry have considered the example of a black hole inside a box filled with radiation. If the density of energy in the box is not very large, then it is favourable for the radiation gas to exist alone, without a black hole. However, there is a turning point at which the density becomes high enough and a black hole condenses, having then roughly $97.7\%$ of the energy available in the box. I should point out, however, that the presence of Hawking radiation is extremely necessary for this argument, since that is what allows the black hole to be in thermal equilibrium with something. Furthermore, it is also essential in arguing what is the entropy of a black hole, as I explained in this post.
A: On the contrary, black holes are the objects in the universe with the highest entropy. According to the Hawking-Bekenstein formula, the entropy $S$  of a black hole is proportional to its surface $A$ which is by swallowing matter constantly increasing as does entropy:
$$ S= \frac{k_BA c^3 }{4 G\hbar }$$
using the usual constants as $c$ speed of light, $k_B$ Boltzmann's constant,
$G$ gravitational constant and $\hbar$ Planck's constant.
So black holes fulfill perfectly the second law of thermodynamics and provide a huge contribution to the entropy of the universe.
