The question is not fully clear to me but I think it may be due to a misunderstanding of certain topics.

I read in my book that any system tends to become disordered or tends to become more probable and this decides the spontaneity of a process.

I personally think that we should first introduce the second law of thermodynamics and with that define entropy then speak of the 'disorder' / statistical interpretation.

The second law of thermodynamics states that for any spontaneous process, the change in the quantity known as entropy must be always positive. There is proof of this using statistical mechanics which you can see here (see here)

Now, depending on the constraints on the system, we can use some potential functions to study how the system will spontaneously evolve. A familiar example is that for the conditions of a mechanical system, we can derive that potential energy is the potential that determines the time evolution of the system. (see here)

Similarly, If we have a chemical system with constant temperature and pressure, the Gibbs free energy is the potential determining the process. I wrote a detailed derivation about it (here).

Interpetation of entropy

We can give a meaningful interpretation of entropy using statistical mechanics. In statistical mechanics, entropy is considered a measure of the number of states of a system, so as we increase states the entropy can be said to increase. I have found a gentle introduction for it here

But I would like to know that if entropy exists then why does a closed system exist? I am asking this question because the system tends to become free but we also know that a close system exists. So, shouldn't all close systems become open systems themselves?

Let us first get some definitions so it is clear what we are speaking,

Open system: Physical system that has external interactions.

Closed system: A closed system is a physical system that does not allow the transfer of matter in or out of the system

I think you are thinking that the number of states increases, the size of the system itself should increase and this in a limiting case would somehow break the boundary of the container itself. If so, this stems from misunderstanding the definition of a closed system as literally a 'system with rigid boundary does not allow mass transfer' rather than just 'a system which does not allow mass transfer'.

However, while it may not be necessary, there is indeed an entropy increase associated with a certain expansion process of an ideal gas (see from 22:50 of this video)

The question is not fully clear to me but I think it may be due to a misunderstanding of certain topics.

I read in my book that any system tends to become disordered or tends to become more probable and this decides the spontaneity of a process.

I personally think that we should first introduce the second law of thermodynamics and with that define entropy then speak of the 'disorder' / statistical interpretation.

The second law of thermodynamics states that for any spontaneous process, the change in the quantity known as entropy must be always positive. There is proof of this using statistical mechanics which you can see here (see here)

Now, depending on the constraints on the system, we can use some potential functions to study how the system will spontaneously evolve. A familiar example is that for the conditions of a mechanical system, we can derive that potential energy is the potential that determines the time evolution of the system. (see here)

Similarly, If we have a chemical system with constant temperature and pressure, the Gibbs free energy is the potential determining the process. I wrote a detailed derivation about it (here).

Interpetation of entropy

We can give a meaningful interpretation of entropy using statistical mechanics. In statistical mechanics, entropy is considered a measure of the number of states of a system, so as we increase states the entropy can be said to increase. I have found a gentle introduction for it here

But I would like to know that if entropy exists then why does a closed system exist? I am asking this question because the system tends to become free but we also know that a close system exists. So, shouldn't all close systems become open systems themselves?

Let us first get some definitions so it is clear what we are speaking,

In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter. -wiki

Open system: Physical system that has external interactions.-wiki

Closed system: A closed system is a physical system that does not allow the transfer of matter in or out of the system.-wiki

Entropy is a quantity directly associated with heat transfer, not mass transfer. I have cited an interpretation for it below.

As a substance is heated, it gains kinetic energy, resulting in increased molecular motion and a broader distribution of molecular speeds. This increases the number of microstates possible for the system. Increasing the number of molecules in a system also increases the number of microstates, as now there are more possible arrangements of the molecules. As well, increasing the volume of a substance increases the number of positions where each molecule could be, which increases the number of microstates. Therefore, any change that results in a higher temperature, more molecules, or a larger volume yields an increase in entropy. Source