R function to give me $P(XI have this empirical discrete distribution with the respective percentiles (picture below).
I want to know a R function which gives me $P(X\lt0.58)$ instead of $P(X\le 0.58)$ (given by ECDF function).
The ECDF function gives me around $0.89$ and $0.90$ but I want something between $0.83$ and $0.84$ (see the picture below).
Is there any functions that does this?

 A: There is a statistical question here.
Let the cumulative distribution function of a random variable be $F_X$, defined as
$$F_X(x) = \Pr(X \le x).$$
What is wanted is a variant of this with a strict inequality,
$$G_X(x) = \Pr(X \lt x).$$
The two differ when there is a nonzero chance that $X=x.$
Notice that the event $X \lt x$ is the same as the event $-X \gt -x,$ which is the complement of the event $-X \le -x.$  Therefore since the chance of an event and the chance of its complement must sum to unity,

$$G_X(x) = 1 - \Pr(-X \le -x) = 1 - F_{-X}(-x).$$

In this way we may find $G_X$ without having to do any more programming simply by computing the empirical CDF for the data $-X.$
In R, for instance, the empirical distribution $F$ of data x would be computed as
f <- ecdf(x)

Consequently we may compute $G$ as
g <- function(a) 1 - (ecdf(-x))(-a)

Here is an illustration of the difference using a dataset much like the one in the question with $x_0=0.58$ the value at which $F_X$ and $G_X$ are to be computed.

In this example, $F_X(0.58)=0.9$ while $G_X(0.58)=0.8.$  You can see that $F_X$ gives the height of the solid dot at $x_0$ while $G_X$ gives the height of the dot immediately to its left.
The dataset x consists of these 30 numbers:
0.24(7) 0.25(2) 0.26 0.27 0.28 0.29(2) 0.30 0.31 0.37 0.39
0.40 0.41 0.44(2) 0.49 0.52 0.58(3) 0.59 0.61 0.78

The values in parentheses give the counts of duplicated values.
