Given a real value $M>0$, I want to compute the greatest value of $\epsilon$ strictly smaller than $M$. Given the assumption that the computational model is Real-RAM, how to find a real number sufficiently close to $M$?
In Real RAM precision is infinite, this comes straight from definition: it uses exact real numbers. As you have noticed this is purely theoretical model. It is also worth notting that real-RAM model gives enormous computational boost from standard RAM model where each cell uses only fixed length, called machine word.
For hardware (practical one), using something like IEEE754, these are not real numbers, but fixed-precision representation, with sign, significand and exponent. Common float has about seven digits of precision. There are types using 24, 32, 64, 80, 128... bits.
If you want to model something with practical indication in mind, do not use real-RAM as it is too powerful.